Chapter 5, Problem 32A

(a)

Interpretation Introduction

Interpretation: The answer to the correct number of significant digits to be calculated.

Concept introduction: Scientific notation is quantitative information is called a measurement and exists of a number and a unit. By using scientific notation too large or too small numbers are conveniently expressed.

Answer to Problem 32A

Significant digit is 52.36

Explanation of Solution

In final result number of significant figures is the same as that in the measurement with smallest number of significant figures.

The given digits are $44.2124+0.81+7.335$

Calculations of these digits are as follows:

  $44.2124+0.81+7.335\text{=52}\text{.3574}$

0.81 has two decimal places. Thus after decimal point the answer should be reported to two digits 52.36

(b)

Interpretation Introduction

Interpretation: The answer to the correct number of significant digits to be calculated.

Concept introduction: Scientific notation is quantitative information is called a measurement and exists of a number and a unit. By using scientific notation too large or too small numbers are conveniently expressed.

Answer to Problem 32A

Significant digit is 10.90

Explanation of Solution

In final result number of significant figures is the same as that in the measurement with smallest number of significant figures.

The given digits are $9.7789+3.3315-2.21$

Calculations of these digits are as follows:

  $9.7789+3.3315-2.21\text{=10}\text{.9004}$

2.21 has two decimal places. Thus after decimal point the answer should be reported to two digits 10.90

(c)

Interpretation Introduction

Interpretation: The answer to the correct number of significant digits to be calculated.

Concept introduction: Scientific notation is quantitative information is called a measurement and exists of a number and a unit. By using scientific notation too large or too small numbers are conveniently expressed.

Answer to Problem 32A

Significant digit is 5.25

Explanation of Solution

In final result number of significant figures is the same as that in the measurement with smallest number of significant figures.

The given digits are $0.8891+0.225+4.14$

Calculations of these digits are as follows:

  $0.8891+0.225+4.14\text{=5}\text{.2541}$

4.14 has two decimal places. Thus after decimal point the answer should be reported to two digits 5.25

(d)

Interpretation Introduction

Interpretation: The answer to the correct number of significant digits to be calculated.

Concept introduction: Scientific notation is quantitative information is called a measurement and exists of a number and a unit. By using scientific notation too large or too small numbers are conveniently expressed.

Answer to Problem 32A

Significant digit is 6.5

Explanation of Solution

In final result number of significant figures is the same as that in the measurement with smallest number of significant figures.

The given digits are $\left(7.223+9.14+3.7795\right)/3.1$

Calculations of these digits are as follows:

  $\begin{array}{c}\frac{\left(7.223+9.14+3.7795\right)}{3.1}=\frac{20.1425}{3.1}\\ \text{=6}\text{.49758065}\end{array}$

3.1 has one decimal places. Thus after decimal point the answer should be reported to one digit 6.5