Chapter 2, Problem 83UTC

The chapter sections to review are shown in parentheses at the end of each problem.
In which of the following pairs do both numbers contain the same number of significant figures? (2.2)
$\begin{array}{l}a.2.0500mand0.0205m\\ b.600.0\text{}Kand60K\\ c.0.00075sand75000s\\ d.6.240Land6.240\times {10}^{-2}L\end{array}$

Interpretation Introduction

To determine: The pairs of numbers that contain the same number of significant figures

Answer to Problem 83UTC

Solution:

c) 0.000 75 s and 75 000 s

d) 6.240 L and 6.240 × 10-2 L

Explanation of Solution

A number is significant if it is:

• Non-zero digit.
• Any zeros between two or more non-zero digits.
• Trailing zeroes in the decimal number.

Also, note that zero placed after a non-zero digit without any decimal is simply a place holder and insignificant. Therefore, as per the above rules one can write:

a)

Number	Significant Figures
2.0500 m	5
0.0205 m	3

b)

Number	Significant Figures
600.0 K	4
60 K	1

c)

Number	Significant Figures
0.000 75 s	2
75 000 s	2

d)

Number	Significant Figures
6.240 L	4
6.240 × 10-2 L	4

Conclusion

The pairs of numbers in (c) and (d) have the same significant figures.