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?

a) (a) 2 (b) 1% (c) Significant figures
b) (a) 2 (b) 1% (c) Significant figures
c) (a) 2 (b) 1% (c) Significant figures

Answer 1

The numbers 99 and 100 each have two significant figures. The percent uncertainty for both numbers with an uncertainty of 1 is 1%. Percent uncertainties provide a more meaningful expression of accuracy than significant figures do.

Step-by-step explanation:

When assessing the number of significant figures in a number, we look at all the digits that are known with certainty plus the first uncertain digit. For the numbers 99 and 100, each contains two significant figures. The trailing zeros after a whole number without a decimal point are not considered significant.

To calculate the percent uncertainty, we divide the uncertainty by the measured value and then multiply by 100. For both numbers 99 and 100 with an uncertainty of 1, the percent uncertainty is 1% for each (1/99 * 100 = ~1.01% and 1/100 * 100 = 1%).

When expressing the accuracy of these numbers, percent uncertainties are more meaningful because they give a clearer indication of the uncertainty in abouteaboutof the number. On the other hand, the number of significant figures is simply an indication of the resolution of the number and does not directly inform about the precision of the measurement.