# Question #6af5d

Sep 18, 2015

The answer must have three sig figs.

#### Explanation:

You need to take into account two rules for finding the number of significant figures an operation produces.

First, you have multiplication, for which you know that the answer cannot have more sig figs than the least number of sig figs you have for the numbers that are being multiplied.

In the first case, you have

$12.95 \to$ four sig figs
$0.109 \to$ three sig figs

The answer should only have three sig figs.

For the second multiplication, you have

$3.177 \to$ four sig figs;
$0.025 \to$ two sig figs

This time, the answer should only have two sig figs.

This means that you get

$12.95 \cdot 0.109 - 3.177 \cdot 0.025 = 1.41155 - 0.079425$

Round these off to the correct number of sig figs to get

$1.41 - 0.079$

Now you need to use the rules for finding the number of sig figs when you're subtracting two decimal numbers.

To find that, arrange the two numbers like this

$1.41$
$0.079$

Now, the last significant gidit in the result will correspond to the leftmost last significant digit of each number. The last significant digits of those numbers are

$1.4 \textcolor{red}{1}$
$0.07 \textcolor{red}{9}$

The one's that's furthest to the left is $\textcolor{red}{1}$. This means that the answer must be rounded off at the hundreths mark.

$1.41 - 0.079 = 1.331$

Rounded to the hundreths mark will result in

$1.41 - 0.079 = \textcolor{g r e e n}{1.33}$