Chapter 3, Problem 2STP

Interpretation Introduction

Interpretation : The answer in two significant figures is to be represented.

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

Answer to Problem 2STP

Option (C).

The answer that represents the measurement rounded to two significant figures is $4.28\times {10}^{-3}\text{g}$ .

Explanation of Solution

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

Because calculated results frequently depend on the number of significant figures in the values used in the calculation, measurements must always be reported to the right number of significant figures.

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 $0.00428\text{g}$ .

According to the rules, the significant figure is $4.28\times {10}^{-3}\text{g}$ .

Conclusion

Option (A): The answer would be option A only if the question is $4280\text{g}$ .

Option (B): The answer would be option B only if the question is $4300\text{g}$ .

Option (D): The answer would be option D only if the question is $0.004\text{g}$ .