# Question 15837

Feb 10, 2016

The uncertainty in the sum $\text{(0.032 ± 0.001 g) + (0.033 ± 0.001 g)}$ is $\text{±0.002 g}$.The average of the two measurements is $\text{0.032 g}$, with an uncertainty of $\text{ ± 0.001) g}$

#### Explanation:

The units don't matter, so let's deal with just the numbers.

$\text{0.032 ± 0.001}$
$\text{0.033 ± 0.001}$
stackrel(——————)("0.065 ± 0.002")

The sum of the two numbers is $0.065$, with an uncertainty of ± 0.002.

The average of the two numbers is

"0.065 ± 0.002"/2 = 0.032 ± 0.001#

Your uncertainty is in the third decimal place, so you can have no more than three decimal places.

You must round off your calculator's answer of $0.0325$ to $0.032$.