Chapter 17, Problem 106A

(a)

Interpretation Introduction

Interpretation: The result of calculation with the correct significant figure is to be calculated.

Concept Introduction : Significant figures are the figures in a number that expresses the value or the magnitude of a quantity to a specific degree of accuracy.

Rules for significant figures are

Digits from 1 to 9 are always significant and have an infinite number of significant figures.

All non-zero numbers are always significant.

All zeros between integers are always significant.

All zeros preceding the first integers are never significant.

All zeros after the decimal point are always significant.

Answer to Problem 106A

The given calculation $6.723\text{ m}\times 1.04\text{ m}$ will result of $\text{6}{\text{.99 m}}^2$

Explanation of Solution

The multiplication rule is the least precise number that determines the number of significant figures in the answer. As $1.04\text{ m}$ has three significant figures, thus the result $\text{6}{\text{.99 m}}^2$ also has three significant figures.

(b)

Interpretation Introduction

Interpretation: The result of calculation with the correct significant figure is to be calculated.

Concept Introduction : Significant figures are the figures in a number that expresses the value or the magnitude of a quantity to a specific degree of accuracy.

Rules for significant figures are

Digits from 1 to 9 are always significant and have an infinite number of significant figures.

All non-zero numbers are always significant.

All zeros between integers are always significant.

All zeros preceding the first integers are never significant.

All zeros after the decimal point are always significant.

Answer to Problem 106A

The given calculation $\text{8}\text{.934 g}+\text{0}\text{.2005 g}+1.55\text{ g}$ will result of $10.68\text{ g}$

Explanation of Solution

The addition rule is that the number with the least decimal places determines the number of significant figures in the answer. As $1.55\text{ g}$ has two decimal places, thus the result $10.68\text{ g}$ will have two decimal places.

(c)

Interpretation Introduction

Interpretation: The result of calculation with the correct significant figure is to be calculated.

Concept Introduction : Significant figures are the figures in a number that expresses the value or the magnitude of a quantity to a specific degree of accuracy.

Rules for significant figures are

Digits from 1 to 9 are always significant and have an infinite number of significant figures.

All non-zero numbers are always significant.

All zeros between integers are always significant.

All zeros preceding the first integers are never significant.

All zeros after the decimal point are always significant.

Answer to Problem 106A

The given calculation $\text{864 m}÷2.4\text{ s}$ will have a result of $\text{3}\text{.6}\times {\text{10}}^2\text{m/s}$

Explanation of Solution

The rule for division is the least precise number determines the number of significant figures in the answer. As $2.4$ has two significant figures, thus the result $\text{3}\text{.6}\times {\text{10}}^2\text{m/s}$ will have two significant figures.

(d)

Interpretation Introduction

Interpretation: The result of calculation with the correct significant figure is to be calculated.

Concept Introduction : Significant figures are the figures in a number that expresses the value or the magnitude of a quantity to a specific degree of accuracy.

Rules for significant figures are

Digits from 1 to 9 are always significant and have an infinite number of significant figures.

All non-zero numbers are always significant. For example, 323, 3.23, and 32.3 all have three significant figures.

All zeros between integers are always significant. For example, 4004, 4.004, and 40.04 all have four significant figures.

All zeros preceding the first integers are never significant. For example, 0.00087 has two significant figures.

All zeros after the decimal point are always significant. For example, 8.900, 89.00, and 890.0 all have four significant figures.

Answer to Problem 106A

The given calculation $9.258\text{°C}-4.82\text{°C}$ will have a result of $4.44\text{°C}$

Explanation of Solution

The rule for subtraction is that the number with the least decimal places determines the number of significant figures in the answer. As $4.82\text{°C}$ has two decimal places, thus, the result $4.44\text{°C}$ will have two decimal places.