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) 1; (b) 1%; (c) Percent uncertainties
b) (a) 2; (b) 1%; (c) Significant figures
c) (a) 2; (b) 2%; (c) Percent uncertainties
d) (a) 2; (b) 1%; (c) Both significant figures and percent uncertainties

Answer 1

The numbers 99 and 100 both have two significant figures, with a 1% uncertainty for each. Percent uncertainties are a more meaningful way to express the accuracy of these numbers as they provide a proportional understanding of uncertainty.

Step-by-step explanation:

To answer question 18: (a) The number 99 has two significant figures, and the number 100 also has two significant figures if we consider it as 1.00 x 10² in scientific notation, where trailing zeros signify precision.

However, if the number 100 is not given to imply precision, it may be interpreted as having only one significant figure.

(b) To calculate the percent uncertainty, we divide the uncertainty (1) by the number and then multiply by 100%. For 99, the percent uncertainty is roughly 1.01%, and for 100, it is exactly 1%.

(c) Because of the different scales of these numbers, using percent uncertainties is likely more meaningful as it gives a clearer idea of proportionate uncertainty rather than just the count of significant figures which does not reflect the size of the number.