# Using the rules for significant figures, what do you get when you subtract 15.54 from 508.9538?

Jul 6, 2016

$- 493.41$

#### Explanation:

The thing to remember when adding or subtracting numbers is that only the decimal part of the number matters.

In other words, all you have to do is inspect the significant figures listed to the right of the decimal point and keep in mind that the answer cannot have more decimal places than the number with the least decimal places.

In your case, you will have

$\textcolor{w h i t e}{1} 15 \text{."color(red)(54) color(white)(11)->" }$ two decimal places

$508 \text{."color(red)(9538) ->" }$ four decimal places

Right from the start you know that the answer must have two decimal places, since that is how many decimal places you have for the least precise measurement.

So, perform the subtraction to get

$15.54 - 508.9538 = - 493.4138$

Now, the result has four decimal places, which means that you're going to have to round it to match the fact that you can only have two decimal places.

Count two decimals

$- 493 \text{.} \textcolor{red}{41} \textcolor{b l u e}{3} 8$

Since the third decimal, i.e. $\textcolor{b l u e}{3}$, is smaller than $5$, you can round this off to

$- 493 \text{.} \textcolor{red}{41}$

Therefore, the result of the subtraction will be

$\textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{15.54 - 508.9538 = - 493.41} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

The answer is rounded to two decimal places.