Question

a) How many significant figures are in the numbers 99 and 100? (b) If the uncertainty in each number is 1, what is the percent uncertainty in each? (c) Which is a more meaningful way to express the accuracy of these two numbers, significant figures or percent uncertainties?

Answer 1

2, 3

1.01, 1

Percentage uncertainty

Explanation:

a) The significant figures in the number 99 is 2

The significant figures in the number 100 is 3

b) Uncertainty in each of the numbers for both the numbers is 1

Percentage uncertainty

99

`\text{Percentage uncertainty}=\frac{\text{Uncertainty}}{Value}* 100 \\\Rightarrow \text{Percentage uncertainty}=(1)/(99)* 100=1.01`

Percentage uncertainty = 1.01

100

`\text{Percentage uncertainty}=\frac{\text{Uncertainty}}{Value}* 100 \\\Rightarrow \text{Percentage uncertainty}=(1)/(100)* 100=1`

Percentage uncertainty = 1

c) Percentage uncertainty is a better way to express the numbers as the significant figures do not show the actual value of the numbers.