To convert the given number 0.0008917 to standard scientific notation. Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10. For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

Question

Want to see more full solutions like this?

Answer 1

Question

Chapter 3, Problem 14CR

(a)

Interpretation Introduction

Interpretation : To convert the given number 0.0008917 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(a)

Expert Solution

Answer to Problem 14CR

8.917×10−4

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number: 0.0008917

Must be converted, so select the first number, ensure the power is correct.

8.917 will be the basis. Since, the decimal shifts 4 positions to the right, the power of ten will be −4 . Thus, the scientific notation is 8.917×10−4 .

(b)

Interpretation Introduction

Interpretation : To convert the given number 2.795×10−4 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(b)

Expert Solution

Answer to Problem 14CR

0.0002795

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

2.7595×10−4 = 0.0002795

When multiplied, we get a decimal number, typically larger than the original expression.

(c)

Interpretation Introduction

Interpretation : To convert the given number 4.913×103 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(c)

Expert Solution

Answer to Problem 14CR

4913

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

4.913×103 = 4913

When multiplied, we get a decimal number, typically larger than the original expression.

(d)

Interpretation Introduction

Interpretation : To convert the given number 85,100,000 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(d)

Expert Solution

Answer to Problem 14CR

8.51×107

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number:

85100000

Must be converted, so select the first number, ensure the power is correct.

8.51 will be the basis. Since, the decimal moves 7 steps to the left, the power of tenth will be+7.

Thus, the scientific notation is 8.51×107 .

(e)

Interpretation Introduction

Interpretation : To convert the given calculation 5.751×105×2.119×10−4 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(e)

Expert Solution

Answer to Problem 14CR

1.219×102

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures

From the second number, 4 significant figures.

Then, 4 significant figures must be kept.

The given number:

Calculate the basis numbers (5.751×2.119) = 12.186369

Multiply the powers:

The tenth base:

10(5−4)= 101=10

Thus, the number becomes 121.863

Keep only 4 significant numbers 121.863, bold digitmust be rounded up. Since, it is followed by digit 6 which is greater than 5, the digit 8 is rounded up to 9. The number becomes 121.9.

Thus, the scientific figure will be 1.219×102

(f)

Interpretation Introduction

Interpretation : To convert the given calculation to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(f)

Expert Solution

Answer to Problem 14CR

3.396×10−9

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures.

From the second number, 4 significant figures.

Then, significant figures must be kept.

The given number:

Calculate the basis numbers (2.7918.219) = 0.3395790

Dividing the powers:

The tenth base:

10(−5−3)= 10−8

Keep only 4 significant numbers 0.3395790 , 5 must be rounded up to 0.3396

0.3396 = 3.396×10−1

Final expression

= (3.396×10−1)( 10−8) = 3.396×10−9

Thus, the scientific notation will be 3.396×10−9 .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

Liquid hexane (CH₂(CH₂) CH3) will react with gaseous oxygen (0₂) to produce gaseous carbon dioxide (CO₂) and 3 4 gaseous water (H₂O). Suppose 66.3 g of hexane is mixed with 66. g of oxygen. Calculate the maximum mass of carbon dioxide that could be produced by the chemical reaction. Be sure your answer has the correct number of significant digits. g x10 X Ś

Units: Include units in your answer when instructed Use SI units only in your answers For example, use Pascals not atmospheres. Numbers: Use either the normal form, such as 132 or 132.5, or the exponential form, which represents 132 as 1.32E+2, represents 5 x 104 as 5E+4 or 5E4, or represents 52 x 10-3 as 5 2E-2, unless instructed otherwise. Do not use the form 5 x 104 If your answer is positive, do not place a "+" sign before your answer. QUESTION 2 Calculate u of 1 mole of helium gas at the top of a mountain (7000 m) under the assumption that the air is just He gas with p = 1 atm at 0m and T= 300 K from 0 m to 7000 m. Calculate your answer in eV, but do not include units in your answer. Write your answer in normal form with 2 decimal places (such as X.XX or XX.XX, etc.). QUESTION 3 A gas and liquid coexist in equilibrium. The mass density pliquid = 1000 pgas Choose the correct relationship between the chemical potentials. a. Pliquid = 1000 µgas O b.Mliquid < Hgas C. Pliquid = Hgas…

At 20oC 25.0 ml of concentrated nitric acid solution was found to have a mass of 32.503 g. What is the calculated density of this solution at 20oC? Show your calculation set-up and result using correct significant figures and proper units. Volume of Nitric acid = 25.0 ml Mass of nitric acid = 32.503 g Density = mass of substance Density= Mass of nitric acid volume of substance volume of nitric acid = 32.503g 25 .0mL = 1.30g/mL (3 sig figures) Using the calculated density of the solution from above, what is the mass of 150 ml. of the solution? Again show your solution set-up with correct significant figures and units.

Answer 2

Question

Chapter 3, Problem 14CR

(a)

Interpretation Introduction

Interpretation : To convert the given number 0.0008917 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(a)

Expert Solution

Answer to Problem 14CR

8.917×10−4

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number: 0.0008917

Must be converted, so select the first number, ensure the power is correct.

8.917 will be the basis. Since, the decimal shifts 4 positions to the right, the power of ten will be −4 . Thus, the scientific notation is 8.917×10−4 .

(b)

Interpretation Introduction

Interpretation : To convert the given number 2.795×10−4 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(b)

Expert Solution

Answer to Problem 14CR

0.0002795

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

2.7595×10−4 = 0.0002795

When multiplied, we get a decimal number, typically larger than the original expression.

(c)

Interpretation Introduction

Interpretation : To convert the given number 4.913×103 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(c)

Expert Solution

Answer to Problem 14CR

4913

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

4.913×103 = 4913

When multiplied, we get a decimal number, typically larger than the original expression.

(d)

Interpretation Introduction

Interpretation : To convert the given number 85,100,000 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(d)

Expert Solution

Answer to Problem 14CR

8.51×107

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number:

85100000

Must be converted, so select the first number, ensure the power is correct.

8.51 will be the basis. Since, the decimal moves 7 steps to the left, the power of tenth will be+7.

Thus, the scientific notation is 8.51×107 .

(e)

Interpretation Introduction

Interpretation : To convert the given calculation 5.751×105×2.119×10−4 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(e)

Expert Solution

Answer to Problem 14CR

1.219×102

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures

From the second number, 4 significant figures.

Then, 4 significant figures must be kept.

The given number:

Calculate the basis numbers (5.751×2.119) = 12.186369

Multiply the powers:

The tenth base:

10(5−4)= 101=10

Thus, the number becomes 121.863

Keep only 4 significant numbers 121.863, bold digitmust be rounded up. Since, it is followed by digit 6 which is greater than 5, the digit 8 is rounded up to 9. The number becomes 121.9.

Thus, the scientific figure will be 1.219×102

(f)

Interpretation Introduction

Interpretation : To convert the given calculation to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(f)

Expert Solution

Answer to Problem 14CR

3.396×10−9

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures.

From the second number, 4 significant figures.

Then, significant figures must be kept.

The given number:

Calculate the basis numbers (2.7918.219) = 0.3395790

Dividing the powers:

The tenth base:

10(−5−3)= 10−8

Keep only 4 significant numbers 0.3395790 , 5 must be rounded up to 0.3396

0.3396 = 3.396×10−1

Final expression

= (3.396×10−1)( 10−8) = 3.396×10−9

Thus, the scientific notation will be 3.396×10−9 .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 3, Problem 14CR

(a)

Interpretation Introduction

Interpretation : To convert the given number 0.0008917 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(a)

Expert Solution

Answer to Problem 14CR

8.917×10−4

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number: 0.0008917

Must be converted, so select the first number, ensure the power is correct.

8.917 will be the basis. Since, the decimal shifts 4 positions to the right, the power of ten will be −4 . Thus, the scientific notation is 8.917×10−4 .

(b)

Interpretation Introduction

Interpretation : To convert the given number 2.795×10−4 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(b)

Expert Solution

Answer to Problem 14CR

0.0002795

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

2.7595×10−4 = 0.0002795

When multiplied, we get a decimal number, typically larger than the original expression.

(c)

Interpretation Introduction

Interpretation : To convert the given number 4.913×103 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(c)

Expert Solution

Answer to Problem 14CR

4913

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

4.913×103 = 4913

When multiplied, we get a decimal number, typically larger than the original expression.

(d)

Interpretation Introduction

Interpretation : To convert the given number 85,100,000 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(d)

Expert Solution

Answer to Problem 14CR

8.51×107

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number:

85100000

Must be converted, so select the first number, ensure the power is correct.

8.51 will be the basis. Since, the decimal moves 7 steps to the left, the power of tenth will be+7.

Thus, the scientific notation is 8.51×107 .

(e)

Interpretation Introduction

Interpretation : To convert the given calculation 5.751×105×2.119×10−4 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(e)

Expert Solution

Answer to Problem 14CR

1.219×102

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures

From the second number, 4 significant figures.

Then, 4 significant figures must be kept.

The given number:

Calculate the basis numbers (5.751×2.119) = 12.186369

Multiply the powers:

The tenth base:

10(5−4)= 101=10

Thus, the number becomes 121.863

Keep only 4 significant numbers 121.863, bold digitmust be rounded up. Since, it is followed by digit 6 which is greater than 5, the digit 8 is rounded up to 9. The number becomes 121.9.

Thus, the scientific figure will be 1.219×102

(f)

Interpretation Introduction

Interpretation : To convert the given calculation to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(f)

Expert Solution

Answer to Problem 14CR

3.396×10−9

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures.

From the second number, 4 significant figures.

Then, significant figures must be kept.

The given number:

Calculate the basis numbers (2.7918.219) = 0.3395790

Dividing the powers:

The tenth base:

10(−5−3)= 10−8

Keep only 4 significant numbers 0.3395790 , 5 must be rounded up to 0.3396

0.3396 = 3.396×10−1

Final expression

= (3.396×10−1)( 10−8) = 3.396×10−9

Thus, the scientific notation will be 3.396×10−9 .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 3, Problem 14CR

(a)

Interpretation Introduction

Interpretation : To convert the given number 0.0008917 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(a)

Expert Solution

Answer to Problem 14CR

8.917×10−4

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number: 0.0008917

Must be converted, so select the first number, ensure the power is correct.

8.917 will be the basis. Since, the decimal shifts 4 positions to the right, the power of ten will be −4 . Thus, the scientific notation is 8.917×10−4 .

(b)

Interpretation Introduction

Interpretation : To convert the given number 2.795×10−4 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(b)

Expert Solution

Answer to Problem 14CR

0.0002795

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

2.7595×10−4 = 0.0002795

When multiplied, we get a decimal number, typically larger than the original expression.

(c)

Interpretation Introduction

Interpretation : To convert the given number 4.913×103 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(c)

Expert Solution

Answer to Problem 14CR

4913

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

4.913×103 = 4913

When multiplied, we get a decimal number, typically larger than the original expression.

(d)

Interpretation Introduction

Interpretation : To convert the given number 85,100,000 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(d)

Expert Solution

Answer to Problem 14CR

8.51×107

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number:

85100000

Must be converted, so select the first number, ensure the power is correct.

8.51 will be the basis. Since, the decimal moves 7 steps to the left, the power of tenth will be+7.

Thus, the scientific notation is 8.51×107 .

(e)

Interpretation Introduction

Interpretation : To convert the given calculation 5.751×105×2.119×10−4 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(e)

Expert Solution

Answer to Problem 14CR

1.219×102

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures

From the second number, 4 significant figures.

Then, 4 significant figures must be kept.

The given number:

Calculate the basis numbers (5.751×2.119) = 12.186369

Multiply the powers:

The tenth base:

10(5−4)= 101=10

Thus, the number becomes 121.863

Keep only 4 significant numbers 121.863, bold digitmust be rounded up. Since, it is followed by digit 6 which is greater than 5, the digit 8 is rounded up to 9. The number becomes 121.9.

Thus, the scientific figure will be 1.219×102

(f)

Interpretation Introduction

Interpretation : To convert the given calculation to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(f)

Expert Solution

Answer to Problem 14CR

3.396×10−9

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures.

From the second number, 4 significant figures.

Then, significant figures must be kept.

The given number:

Calculate the basis numbers (2.7918.219) = 0.3395790

Dividing the powers:

The tenth base:

10(−5−3)= 10−8

Keep only 4 significant numbers 0.3395790 , 5 must be rounded up to 0.3396

0.3396 = 3.396×10−1

Final expression

= (3.396×10−1)( 10−8) = 3.396×10−9

Thus, the scientific notation will be 3.396×10−9 .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 3, Problem 14CR

(a)

Interpretation Introduction

Interpretation : To convert the given number 0.0008917 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(a)

Expert Solution

Answer to Problem 14CR

8.917×10−4

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number: 0.0008917

Must be converted, so select the first number, ensure the power is correct.

8.917 will be the basis. Since, the decimal shifts 4 positions to the right, the power of ten will be −4 . Thus, the scientific notation is 8.917×10−4 .

(b)

Interpretation Introduction

Interpretation : To convert the given number 2.795×10−4 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(b)

Expert Solution

Answer to Problem 14CR

0.0002795

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

2.7595×10−4 = 0.0002795

When multiplied, we get a decimal number, typically larger than the original expression.

(c)

Interpretation Introduction

Interpretation : To convert the given number 4.913×103 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(c)

Expert Solution

Answer to Problem 14CR

4913

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

4.913×103 = 4913

When multiplied, we get a decimal number, typically larger than the original expression.

(d)

Interpretation Introduction

Interpretation : To convert the given number 85,100,000 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(d)

Expert Solution

Answer to Problem 14CR

8.51×107

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number:

85100000

Must be converted, so select the first number, ensure the power is correct.

8.51 will be the basis. Since, the decimal moves 7 steps to the left, the power of tenth will be+7.

Thus, the scientific notation is 8.51×107 .

(e)

Interpretation Introduction

Interpretation : To convert the given calculation 5.751×105×2.119×10−4 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(e)

Expert Solution

Answer to Problem 14CR

1.219×102

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures

From the second number, 4 significant figures.

Then, 4 significant figures must be kept.

The given number:

Calculate the basis numbers (5.751×2.119) = 12.186369

Multiply the powers:

The tenth base:

10(5−4)= 101=10

Thus, the number becomes 121.863

Keep only 4 significant numbers 121.863, bold digitmust be rounded up. Since, it is followed by digit 6 which is greater than 5, the digit 8 is rounded up to 9. The number becomes 121.9.

Thus, the scientific figure will be 1.219×102

(f)

Interpretation Introduction

Interpretation : To convert the given calculation to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(f)

Expert Solution

Answer to Problem 14CR

3.396×10−9

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures.

From the second number, 4 significant figures.

Then, significant figures must be kept.

The given number:

Calculate the basis numbers (2.7918.219) = 0.3395790

Dividing the powers:

The tenth base:

10(−5−3)= 10−8

Keep only 4 significant numbers 0.3395790 , 5 must be rounded up to 0.3396

0.3396 = 3.396×10−1

Final expression

= (3.396×10−1)( 10−8) = 3.396×10−9

Thus, the scientific notation will be 3.396×10−9 .

Answer 6

Chapter 3, Problem 14CR

(a)

Interpretation Introduction

Interpretation : To convert the given number 0.0008917 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(a)

Expert Solution

Answer to Problem 14CR

8.917×10−4

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number: 0.0008917

Must be converted, so select the first number, ensure the power is correct.

8.917 will be the basis. Since, the decimal shifts 4 positions to the right, the power of ten will be −4 . Thus, the scientific notation is 8.917×10−4 .

Answer 7

Chapter 3, Problem 14CR

(a)

Interpretation Introduction

Interpretation : To convert the given number 0.0008917 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

Answer 8

(a)

Expert Solution

Answer to Problem 14CR

8.917×10−4

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number: 0.0008917

Must be converted, so select the first number, ensure the power is correct.

8.917 will be the basis. Since, the decimal shifts 4 positions to the right, the power of ten will be −4 . Thus, the scientific notation is 8.917×10−4 .

Answer 13

(b)

Interpretation Introduction

Interpretation : To convert the given number 2.795×10−4 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(b)

Expert Solution

Answer to Problem 14CR

0.0002795

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

2.7595×10−4 = 0.0002795

When multiplied, we get a decimal number, typically larger than the original expression.

Answer 14

(b)

Interpretation Introduction

Interpretation : To convert the given number 2.795×10−4 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

Answer 15

(b)

Expert Solution

Answer to Problem 14CR

0.0002795

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

2.7595×10−4 = 0.0002795

When multiplied, we get a decimal number, typically larger than the original expression.

Answer 20

(c)

Interpretation Introduction

Interpretation : To convert the given number 4.913×103 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(c)

Expert Solution

Answer to Problem 14CR

4913

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

4.913×103 = 4913

When multiplied, we get a decimal number, typically larger than the original expression.

Answer 21

(c)

Interpretation Introduction

Interpretation : To convert the given number 4.913×103 to ordinary decimal notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

Answer 22

(c)

Expert Solution

Answer to Problem 14CR

4913

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

In order to convert expressions in scientific notation to ordinary decimal notation, we must follow the following rules:

Multiply the given power to the base number.

4.913×103 = 4913

When multiplied, we get a decimal number, typically larger than the original expression.

Answer 27

(d)

Interpretation Introduction

Interpretation : To convert the given number 85,100,000 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(d)

Expert Solution

Answer to Problem 14CR

8.51×107

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number:

85100000

Must be converted, so select the first number, ensure the power is correct.

8.51 will be the basis. Since, the decimal moves 7 steps to the left, the power of tenth will be+7.

Thus, the scientific notation is 8.51×107 .

Answer 28

(d)

Interpretation Introduction

Interpretation : To convert the given number 85,100,000 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

Answer 29

(d)

Expert Solution

Answer to Problem 14CR

8.51×107

Answer 30

(d)

Expert Solution

Answer 31

(d)

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

The given number:

85100000

Must be converted, so select the first number, ensure the power is correct.

8.51 will be the basis. Since, the decimal moves 7 steps to the left, the power of tenth will be+7.

Thus, the scientific notation is 8.51×107 .

Answer 34

(e)

Interpretation Introduction

Interpretation : To convert the given calculation 5.751×105×2.119×10−4 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(e)

Expert Solution

Answer to Problem 14CR

1.219×102

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures

From the second number, 4 significant figures.

Then, 4 significant figures must be kept.

The given number:

Calculate the basis numbers (5.751×2.119) = 12.186369

Multiply the powers:

The tenth base:

10(5−4)= 101=10

Thus, the number becomes 121.863

Keep only 4 significant numbers 121.863, bold digitmust be rounded up. Since, it is followed by digit 6 which is greater than 5, the digit 8 is rounded up to 9. The number becomes 121.9.

Thus, the scientific figure will be 1.219×102

Answer 35

(e)

Interpretation Introduction

Interpretation : To convert the given calculation 5.751×105×2.119×10−4 to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

Answer 36

(e)

Expert Solution

Answer to Problem 14CR

1.219×102

Answer 37

(e)

Expert Solution

Answer 38

(e)

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures

From the second number, 4 significant figures.

Then, 4 significant figures must be kept.

The given number:

Calculate the basis numbers (5.751×2.119) = 12.186369

Multiply the powers:

The tenth base:

10(5−4)= 101=10

Thus, the number becomes 121.863

Keep only 4 significant numbers 121.863, bold digitmust be rounded up. Since, it is followed by digit 6 which is greater than 5, the digit 8 is rounded up to 9. The number becomes 121.9.

Thus, the scientific figure will be 1.219×102

Answer 41

(f)

Interpretation Introduction

Interpretation : To convert the given calculation to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

(f)

Expert Solution

Answer to Problem 14CR

3.396×10−9

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures.

From the second number, 4 significant figures.

Then, significant figures must be kept.

The given number:

Calculate the basis numbers (2.7918.219) = 0.3395790

Dividing the powers:

The tenth base:

10(−5−3)= 10−8

Keep only 4 significant numbers 0.3395790 , 5 must be rounded up to 0.3396

0.3396 = 3.396×10−1

Final expression

= (3.396×10−1)( 10−8) = 3.396×10−9

Thus, the scientific notation will be 3.396×10−9 .

Answer 42

(f)

Interpretation Introduction

Interpretation : To convert the given calculation to standard scientific notation.

Concept Introduction : Scientific notation for a number is written in such a way that large numbers are written in small decimal form which is then multiplied by the power of 10.

For numbers less than 1, the power of 10 in scientific notation has negative exponent and for numbers greater than 1, the power is either zero or has positive exponent.

Answer 43

(f)

Expert Solution

Answer to Problem 14CR

3.396×10−9

Answer 44

(f)

Expert Solution

Answer 45

(f)

Expert Solution

Answer 46

Expert Solution

Answer 47

Explanation of Solution

In order to convert numbers to scientific notation, we must follow the following rules:

Use a single number before the decimal point. All other numbers will be placed after the decimal point.

The basis of expression will be the 10^t^h power. The powers can be any integer number.

For a multiplication or division, significant figures rules must be followed.

The total amount of significant figures in the final result must be equal to the least amount of significant figures in the numbers multiplied or divided.

From the first number, 4 significant figures.

From the second number, 4 significant figures.

Then, significant figures must be kept.

The given number:

Calculate the basis numbers (2.7918.219) = 0.3395790

Dividing the powers:

The tenth base:

10(−5−3)= 10−8