Chapter 1, Problem 39A

(a)

To determine

The number of significant figures in the measurement $0.00003\text{m}$ .

Answer to Problem 39A

The significant digits for the measurement $0.00003\text{m}$ is one.

Explanation of Solution

Introduction:

The number of the digits in the measured physical quantity that describes the accurate measurement of the physical quantity is called significant digits.

The zeros occurring to the left of the last non zero digit is not considered as significant number, so the measurement $0.00003\text{m}$ has only one significant digit.

Conclusion:

Thus, the number of significant figures in the given measurements $0.00003\text{m}$ is one.

(b)

To determine

The number of significant figures in the measurement $64.01\text{fm}$ .

Answer to Problem 39A

The significant digits for the measurement $64.01\text{fm}$ is four.

Explanation of Solution

Introduction:

The number of the significant figures in the measurement describes the accuracy of the measurement.

The zeros between the nonzero digits is considered as the significant digit, so the measurement $64.01\text{fm}$ has four significant digits.

Conclusion:

Thus, the significant digits in the measurement $64.01\text{fm}$ is four.

(c)

To determine

The number of significant figures in the measurement $80.001\text{m}$ .

Answer to Problem 39A

The significant digits for the measurement $80.001\text{m}$ are five.

Explanation of Solution

Introduction:

The accuracy in the measurement depends on the significant digits, so the accuracy of the measurement will be high if the significant digits are more.

The zeros between the nonzero digits are considered as the significant digit, so the measurement $80.001\text{m}$ has five significant digits.

Conclusion:

Thus, the significant digits in the measurement $80.001\text{m}$ is five.

(d)

To determine

The number of significant figures in the measurement $6\times {10}^8\text{kg}$ .

Answer to Problem 39A

The significant digits for the measurement $6\times {10}^8\text{kg}$ is one.

Explanation of Solution

Introduction:

The number of the digits in the measured physical quantity that describes the accurate measurement of the physical quantity is called significant digits.

The zeros that can be shown in the form of power of the 10 are not considered as the significant digits, so the measurement $6\times {10}^8\text{kg}$ has only one significant digit.

Conclusion:

Thus, the number of significant figures in the measurements $6\times {10}^8\text{kg}$ is one.

(e)

To determine

The significant digits for the measurement $4.07\times {10}^{16}\text{m}$ .

Answer to Problem 39A

The significant digits for the measurement $4.07\times {10}^{16}\text{m}$ is one.

Explanation of Solution

Introduction:

The accuracy of the measurement can be increased by the increase in the number of significant digits in the measurement.

The last nonzero digit of the number in the measurement $4.07\times {10}^{16}\text{m}$ is greater than 5, so immediate left number rounded off. The number of significant digits in the measurement $4.07\times {10}^{16}\text{m}$ is only two.

Conclusion:

Thus, the number of significant figures in the measurements $4.07\times {10}^{16}\text{m}$ is two.