Chapter 3.1, Problem 5SP

a)

Interpretation Introduction

Interpretation : The number of significant figures in the given measurement is to be determined.

Concept Introduction : The known digits plus the last estimated digit make up the significant figures in a measurement.

Answer to Problem 5SP

The number of significant figures is 3.

Explanation of Solution

The known digits plus the last, estimated digit make up the significant figures in a measurement.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. The leftmost zeros that exist before nonzero digits are not significant.
4. A zero following a decimal point and to the right of it are both always significant.
5. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
6. In some cases, a number may have an infinite number of significant figures.

The given measurement is ] $143\text{grams}$ .

According to rule 1, the significant figure is 3.

b)

Interpretation Introduction

Interpretation : The number of significant figures in the given measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

Answer to Problem 5SP

The number of significant figures is 2.

Explanation of Solution

The known digits plus the last, estimated digit make up the significant figures in a measurement.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. The leftmost zeros that exist before nonzero digits are not significant.
4. A zero following a decimal point and to the right of it are both always significant.
5. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
6. In some cases, a number may have an infinite number of significant figures.

The given measurement is $\text{0}\text{.074}\text{meter}$ .

According to rule 3, the significant figure is 2.

c)

Interpretation Introduction

Interpretation : The number of significant figures in the given measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

Answer to Problem 5SP

The number of significant figures is 4.

Explanation of Solution

The known digits plus the last, estimated digit make up the significant figures in a measurement.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. The leftmost zeros that exist before nonzero digits are not significant.
4. A zero following a decimal point and to the right of it are both always significant.
5. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
6. In some cases, a number may have an infinite number of significant figures.

The given measurement is $8.750\times {10}^{-2}\text{gram}$ .

According to rule 4, the significant figure is 4.

d)

Interpretation Introduction

Interpretation : The number of significant figures in the given measurement is to be determined.

Concept Introduction : The known digits plus the last, estimated digit make up the significant figures in a measurement.

Answer to Problem 5SP

The number of significant figures is 4.

Explanation of Solution

The known digits plus the last, estimated digit make up the significant figures in a measurement.

There is a set of rules to detect the digits in a significant measured value. The rules are as follows:

1. It is assumed that every nonzero digit in a given measurement is significant.
2. Zeros that come in between nonzero numbers are significant.
3. The leftmost zeros that exist before nonzero digits are not significant.
4. A zero following a decimal point and to the right of it are both always significant.
5. Zeros that are to the left of an understandable decimal point at the rightmost end of measurement are not significant.
6. In some cases, a number may have an infinite number of significant figures.

The given measurement is $1.072\text{meters}$ .

According to rule 2, the significant figure is 4.