Chapter 1, Problem 1.49QP

(a)

Interpretation Introduction

Interpretation: The answer in the correct number of significant figures for the given calculations is to be determined.

Concept introduction: When taking the product of two numbers, the lowest number of significant figures is considered to be the correct number of significant figures for the answer.

To determine: The answer in the correct number of significant figures for the given calculation.

Answer to Problem 1.49QP

Solution

The answer of the given calculation in the correct number of significant figures is $17.4$.

Explanation of Solution

Explanation

Given

The calculation involving multiplication and division in which the value $2.54$ is exact is given as,

$\frac{0.6274\times 1.00\times {10}^3}{2.205\times {\left(2.54\right)}^3}$

The answer of the given calculation is calculated by multiplying and dividing the given numbers.

$\frac{0.6274\times 1.00\times {10}^3}{2.205\times {\left(2.54\right)}^3}=17.3634$

The correct number of significant figure for the given calculation is the significant figures of exact value or the significant figures of the number having lowest significant figures in the calculation. Since, the exact value in the given calculation has three significant figures. Therefore, the significant figures of answer must be three.

The answer for the given calculation is rounded off to the correct number of significant figures by the following rules:

• The first digit from right in the answer is less than five then the digit left to this digit remains unchanged.
• The first digit from right in the answer is more than five then the digit left to this digit is increased by one.
• All non significant digits are removed.

The answer for the given calculation is $17.3634$.

For the given value,

• The left digit is less than five.

Therefore, the first round off value is $17.363$.

For the first round off value,

• The left digit is less than five.

Therefore, the first round off value is $17.36$.

For the second round off value,

• The left digit is greater than five.

Therefore, the first round off value is $17.4$.

Since, the answer $17.4$ has three significant figures. Therefore, this has correct number of significant figures.

(b)

Interpretation Introduction

To determine: The answer in the correct number of significant figures for the given calculation.

Answer to Problem 1.49QP

Solution

The answer of the given calculation in the correct number of significant figures is $72\times 10^{-15}$.

Explanation of Solution

Explanation

Given

The calculation involving multiplication in which the value $12$ is exact is given as,

$6\times {10}^{-18}\times 1.00\times {10}^3\times 12$

The answer of the given calculation is calculated by multiplying and dividing the given numbers.

$6\times {10}^{-18}\times 1.00\times {10}^3\times 12=72\times {10}^{-15}$

The correct number of significant figure for the given calculation is the significant figures of exact value or the significant figures of the number having lowest significant figures in the calculation. Since, the exact value in the given calculation has two significant figures. Therefore, the significant figures of answer must be two.

Since, the answer in the given calculation has two significant figures. Therefore, it has the correct number of significant figures.

(c)

Interpretation Introduction

To determine: The answer in the correct number of significant figures for the given calculation.

Answer to Problem 1.49QP

Solution

The answer of the given calculation in the correct number of significant figures is $5.70\times 10^{-23}$.

Explanation of Solution

Explanation

Given

The calculation involving multiplication and division is given as,

$\frac{4.00\times 58.69}{6.02\times {10}^{23}\times 6.84}$

The answer of the given calculation is calculated by multiplying and dividing the given numbers.

$\frac{4.00\times 58.69}{6.02\times {10}^{23}\times 6.84}=5.70\times {10}^{-23}$

The correct number of significant figure for the given calculation is the significant figures of exact value or the significant figures of the number having lowest significant figures in the calculation. Since, the lowest number of significant figures in the given calculation is three. Therefore, the significant figures of answer must be three.

Since, the answer in the given calculation has three significant figures. Therefore, it has the correct number of significant figures.

(d)

Interpretation Introduction

To determine: The answer in the correct number of significant figures for the given calculation.

Answer to Problem 1.49QP

Solution

The answer of the given calculation in the correct number of significant figures is $35.9\times 10^{-4}$.

Explanation of Solution

Explanation

Given

The calculation involving multiplication and division is given as,

$\frac{26.0\times 60.0÷43.53}{1.000\times {10}^4}$

The answer of the given calculation is calculated by multiplying and dividing the given numbers.

$\frac{26.0\times 60.0÷43.53}{1.000\times {10}^4}=35.8373\times {10}^{-4}$

The correct number of significant figure for the given calculation is the significant figures of exact value or the significant figures of the number having lowest significant figures in the calculation. Since, the lowest number of significant figures in the given calculation is three. Therefore, the significant figures of answer must be three.

The answer for the given calculation is rounded off to the correct number of significant figures by the following rules:

• The first digit from right in the answer is less than five then the digit left to this digit remains unchanged.
• The first digit from right in the answer is more than five then the digit left to this digit is increased by one.
• All non significant digits are removed.

The answer for the given calculation is $35.8373\times {10}^{-4}$.

For the given value,

• The left digit is less than five.

Therefore, the first round off value is $35.837\times {10}^{-4}$.

For the first round off value,

• The left digit is greater than five.

Therefore, the first round off value is $35.84\times {10}^{-4}$.

For the second round off value,

• The left digit is greater than five.

Therefore, the first round off value is $35.9\times {10}^{-4}$.

Since, the answer $35.9\times {10}^{-4}$ has three significant figures. Therefore, this has correct number of significant figures.

Conclusion

1. a. The answer of the given calculation in the correct number of significant figures is $17.4$.
2. b. The answer of the given calculation in the correct number of significant figures is $72\times 10^{-15}$.
3. c. The answer of the given calculation in the correct number of significant figures is $5.70\times 10^{-23}$.
4. d. The answer of the given calculation in the correct number of significant figures is $35.9\times 10^{-4}$