Chapter 1, Problem 19PP

(a)

Interpretation Introduction

Interpretation:

The answer of the operation, in significant figures, is to be determined.

Explanation of Solution

Significant figures are the digit numbers in which the answer is described in accuracy. It starts with a non-zero-digit and has accuracy. In multiplication, division, addition or subtraction, the significant figure of the answer is equal to the significant figure of the number that has the least digits in it.

The given expression is $\frac{8.9\times {10}^4}{1.25\times {10}^5}+0.135$ .

$8.9$ has $2$ significant figures and $1.25$ has $3$ significant figures. Therefore, the result of the division has $2$ significant figures.

$\begin{array}{l}=\frac{8.9\times {10}^4}{1.25\times {10}^5}+0.135\\ =0.712+0.135\end{array}$

$0.712$ has $3$ significant figures and $0.135$ has $3$ significant figures. Therefore, the final answer has $3$ significant figures.

$\begin{array}{l}=0.712+0.135\\ =0.847\end{array}$

The answer of the operation, in significant figures, is $0.847$ .

(b)

Interpretation Introduction

Interpretation:

The answer of the operation, in significant figures, is to be determined.

Explanation of Solution

The given expression is $\frac{\left(52.50-2.0\right)}{3.00}$ .

$52.50$ has $4$ significant figures and $2.0$ has only $2$ significant figures. Therefore, the result of subtraction has $2$ significant figures.

$\begin{array}{l}=\frac{\left(52.50-2.0\right)}{3.00}\\ =\frac{51}{3.00}\end{array}$

$51$ has $2$ significant figures and $3.00$ has $3$ significant figures. Therefore, the final answer has $2$ significant figures.

$\begin{array}{l}=\frac{51}{3.00}\\ =17\end{array}$

The answer of the operation in, significant figures, is $17$ .

(c)

Interpretation Introduction

Interpretation:

The answer of the operation, in significant figures, is to be determined.

Explanation of Solution

The given expression is $\frac{9.25}{{\left(1.9\right)}^3}-\frac{19.64}{{\left(2.50\right)}^3}$ .

$9.25$ has $3$ significant figures and $1.9$ has $2$ significant figures. Therefore, the result has $2$ significant figures. $19.64$ has $4$ significant figures and $2.50$ has $3$ significant figures. Therefore, the result has $3$ significant figures.

$\begin{array}{l}=\frac{9.25}{{\left(1.9\right)}^3}-\frac{19.64}{{\left(2.50\right)}^3}\\ =1.3-1.26\end{array}$

$1.3$ has $2$ significant figures and $1.26$ has $3$ significant figures. Therefore, the final answer has $2$ significant figures.

$\begin{array}{l}=1.3-1.26\\ =0.040\end{array}$

The answer of the operation, in significant figures, is $0.040$ .

(d)

Interpretation Introduction

Interpretation:

The answer of the operation, in significant figures, is to be determined.

Explanation of Solution

The given expression is $\left(6.2{\text{ g mL}}^{-1}\times 1.95\text{ g mL}\right)+0.6\text{ g}$ .

$6.2{\text{ g mL}}^{-1}$ has $2$ significant figures and $1.95\text{ g mL}$ has $3$ significant figures. Therefore, the result has $2$ significant figures.

$\begin{array}{l}=\left(6.2{\text{ g mL}}^{-1}\times 1.95\text{ g mL}\right)+0.6\text{ g}\\ =\text{12 g}+0.6\text{ g}\end{array}$

$12\text{ g}$ has $2$ significant figures and $0.6\text{ g}$ has $2$ significant figures. Therefore, the final answer has $2$ significant figures.

$\begin{array}{l}=\text{12 g}+0.6\text{ g}\\ =12.6\text{ g}\\ =\text{1}3\text{ g}\end{array}$

The answer of the operation, in significant figures, is $\text{1}3\text{ g}$ .