# Interesting Fact About Decimal Number

### 0.999… is equal to 1

This is a hard one to wrap your head around. 0.999… with infinite decimals, often written as 0.(9) is actually equal to 1. How does that work? Well, there’s a couple of ways you can look at it.

Firstly, one divided by three is 0.333…, with infinite decimals. Then, 0.(3) multiplied by 3 is 0.(9)… but it’s also 1 because a number multiplied and divided by the same number remains unchanged. To put it mathematically:

1:3 = 0.333, or 0.(3)

0.(3) x 3 = 0.(9),

but 1:3*3 = 1, so 1 = 0.(9).

You can also think about it this way:

If that’s not convincing enough, then think about it another way. If 0.(9) is smaller than 1, then what would you have to add to it to get to 1? No matter what number you add, it’s still not small enough because such a number doesn’t exist – 0.999… = 1.