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

##### 1 Answer

#### 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

#color(white)(1)15"."color(red)(54) color(white)(11)->" "# two decimal places

#508"."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"."color(red)(41)color(blue)(3)8#

Since the third decimal, i.e. **smaller** than

#-493"."color(red)(41)#

Therefore, the result of the subtraction will be

#color(green)(|bar(ul(color(white)(a/a)color(black)(15.54 - 508.9538 = - 493.41)color(white)(a/a)|)))#

The answer is *rounded to two decimal places*.