# How can I perform the following operation 32500 + 26 823 - 56 000 taking into account the number of significant figures?

## I know that the correct answer is 3 300 or 3.3 x 10^3, but I do not understand why. Please clarify? Thanks!

Oct 4, 2016

Here's how you can do that.

#### Explanation:

The first thing to note here is that the correct answer is not $3300$ or $3.3 \times {10}^{3}$, believe it or not.

What you need to remember about addition and subtraction with significant figures is that you only need to examine the decimal portion of the numbers, i.e. to the right of the decimal point.

In this case, you have

$32500 \to$ no decimal point, i.e. no decimals

$26823 \to$ no decimal point, i.e. no decimals

$56000 \to$ no decimal point, i.e. no decimals

This means that the answer cannot have a decimal point. In other words, the answer will be rounded to zero decimals. Consequently, you will have

$32500 + 26823 - 56000 = 3323$

That is the correct answer here, a value with no decimals. This value has a total of four sig figs, all given by its four non-zero digits.

If, for some reason, you want to round this off to two sig figs, then the answer would be $3300$, or $3.3 \times {10}^{3}$ expressed in scientific notation.

So remember, for addition and subtraction, you only have to look at the decimal portion of the numbers, not at the total number of sig figs they each have.