Chemistry for Today: General, Organic, and Biochemistry
Chemistry for Today: General, Organic, and Biochemistry
9th Edition
ISBN: 9781305960060
Author: Spencer L. Seager, Michael R. Slabaugh, Maren S. Hansen
Publisher: Cengage Learning
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Chapter 1, Problem 1.57E

Express each of the following numbers using scientific notation, then carry out the multiplication. Express each answer using scientific notation.

a. ( 538 ) ( 0.154 )

b. ( 600 ) ( 524 )

c. ( 22.8 ) ( 341 )

d. ( 23.6 ) ( 0.047 )

Expert Solution
Check Mark
Interpretation Introduction

(a)

Interpretation:

The given numbers are to be expressed using scientific notation and also the answer of the given multiplication is to be expressed by using scientific notation.

Concept introduction:

Scientific notation is used to write large numbers or small numbers as the product of a non-exponential term and exponential term in the form of M×10n. The M is any number between 1 to 10 written with a decimal after first non-zero digit in the number and n is the exponent which may be positive or negative.

Answer to Problem 1.57E

The given multiplication expressed using scientific notation is shown below.

(5.38×102)(1.54×101)

The answer of the given multiplication expressed by using scientific notation is 8.2852×101.

Explanation of Solution

The given question is,

(538)(0.154)

To express the number 538 using the scientific notation, the non-zero digits should be separated by decimal and only one non-zero digit should be written before decimal. Thus, the number can be expressed as 5.38×102.

To express the number 0.154 using the scientific notation, decimal is moved one place to the right and only one non-zero digit should be written before decimal. The number of places that the decimal moves to the right becomes exponent n in the form of M×10n. Thus, the number can be expressed as 1.54×101.

The given multiplication expressed using scientific notation is shown below.

(5.38×102)(1.54×101)

The multiplication can be expressed as follows:

(a×10y)(b×10z)=(a×b)(10y+z)

The answer of the given multiplication can be calculated as follows:

(5.38×1.54)(1021)=8.2852×101

Hence, the answer of the given multiplication is 8.2852×101.

Conclusion

The given multiplication expressed using scientific notation is shown below.

(5.38×102)(1.54×101)

The answer of the given multiplication expressed by using scientific notation is 8.2852×101.

Expert Solution
Check Mark
Interpretation Introduction

(b)

Interpretation:

The given numbers are to be expressed using scientific notation and also the answer of the given multiplication is to be expressed by using scientific notation.

Concept introduction:

Scientific notation is used to write large numbers or small numbers as the product of a non-exponential term and exponential term in the form of M×10n. The M is any number between 1 to 10 written with a decimal after first non-zero digit in the number and n is the exponent which may be positive or negative.

Answer to Problem 1.57E

The given multiplication expressed using scientific notation is shown below.

(6.00×102)(5.24×102)

The answer of the given multiplication expressed by using scientific notation is 3.144×105.

Explanation of Solution

The given question is,

(600)(524)

To express the number 600 using the scientific notation, the non-zero digits should be separated by decimal and only one non-zero digit should be written before decimal. Thus, the number can be expressed as 6.00×102.

To express the number 524 using the scientific notation, the non-zero digits should be separated by decimal and only one non-zero digit should be written before decimal. Thus, the number can be expressed as 5.24×102.

The given multiplication expressed using scientific notation is shown below.

(6.00×102)(5.24×102)

The multiplications can be expressed as follows:

(a×10y)(b×10z)=(a×b)(10y+z)

The answer of the given multiplication can be calculated as follows:

(6.00×5.24)(102+2)=31.44×104

The above answer is adjusted to a standard position. The decimal is shifted one place to the left and the power of 10 is changed from 4 to 5. Hence, the answer of the given multiplication is 3.144×105.

Conclusion

The given multiplication expressed using scientific notation is shown below.

(6.00×102)(5.24×102)

The answer of the given multiplication expressed by using scientific notation is 3.144×105.

Expert Solution
Check Mark
Interpretation Introduction

(c)

Interpretation:

The given numbers are to be expressed using scientific notation and also the answer of the given multiplication is to be expressed by using scientific notation.

Concept introduction:

Scientific notation is used to write large numbers or small numbers as the product of a non-exponential term and exponential term in the form of M×10n. The M is any number between 1 to 10 written with a decimal after first non-zero digit in the number and n is the exponent which may be positive or negative.

Answer to Problem 1.57E

The given multiplication expressed using scientific notation is shown below.

(2.28×101)(3.41×102)

The answer of the given multiplication expressed by using scientific notation is 7.7748×103.

Explanation of Solution

The given question is,

(22.8)(341)

To express the number 22.8 using the scientific notation, the non-zero digits should be separated by decimal and only one non-zero digit should be written before decimal. Thus, the number can be expressed as 7.7748×103.

To express the number 341 using the scientific notation, the non-zero digits should be separated by decimal and only one non-zero digit should be written before decimal. Thus, the number can be expressed as 3.41×102.

The given multiplication expressed using scientific notation is shown below.

(2.28×101)(3.41×102)

The multiplications can be expressed as follows:

(a×10y)(b×10z)=(a×b)(10y+z)

The answer of the given multiplication can be calculated as follows:

(2.28×3.41)(101+2)=7.7748×103

Hence, the answer of the given multiplication is 7.7748×103.

Conclusion

The given multiplication expressed using scientific notation is shown below.

(2.28×101)(3.41×102)

The answer of the given multiplication expressed by using scientific notation is 7.7748×103.

Expert Solution
Check Mark
Interpretation Introduction

(d)

Interpretation:

The given numbers are to be expressed using scientific notation and also the answer of the given multiplication is to be expressed by using scientific notation.

Concept introduction:

Scientific notation is used to write large numbers or small numbers as the product of a non-exponential term and exponential term in the form of M×10n. The M is any number between 1 to 10 written with a decimal after first non-zero digit in the number and n is the exponent which may be positive or negative.

Answer to Problem 1.57E

The given multiplication expressed using scientific notation is shown below.

(2.36×101)(4.7×102)

The answer of the given multiplication expressed by using scientific notation is 1.1092×100.

Explanation of Solution

The given question is,

(23.6)(0.047)

To express the number 23.6 using the scientific notation, the non-zero digits should be separated by decimal and only one non-zero digit should be written before decimal. Thus, the number can be expressed as 2.36×101.

To express the number 0.047 using the scientific notation, decimal moves two places to the right and only one non-zero digit should be written before decimal. The number of places that the decimal moves to the right becomes exponent n in the form of M×10n. Thus, the number can be expressed as 4.7×102.

The given multiplication expressed using scientific notation is shown below.

(2.36×101)(4.7×102)

The multiplications can be expressed as follows:

(a×10y)(b×10z)=(a×b)(10y+z)

The answer of the given multiplication can be calculated as follows:

(2.36×4.7)(1012)=11.092×101

The above answer is adjusted to a standard position. The decimal is shifted towards one place left and the power of 10 is changed from 1 to 0. Hence, the answer of the given multiplication is 1.1092×100.

Conclusion

The given multiplication expressed using scientific notation is shown below.

(2.36×101)(4.7×102)

The answer of the given multiplication expressed by using scientific notation is 1.1092×100.

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Chapter 1 Solutions

Chemistry for Today: General, Organic, and Biochemistry

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