# Fractional part

In the previous post I talked about the floor and ceiling functions. Go check them out if you haven’t already! We are going to need them to learn about the fractional part.

**What is fractional part?**

The fractional part of a *positive* number is the part after the decimal, i.e. the decimal part. We can write the fractional part of a number *x* as

Here are some examples:

If you noticed, the fractional part of 2.6 is 0.6, which is 2.6-2, and the same happens for the other examples. This means that the result is the input – the integer part, and, as we saw in the previous post, the integer part of a real number is given by the floor function.

*For real numbers, the fractional part can be defined as*

And for the first example we have:

Another definition I figured out playing around with numbers makes use of the ceiling function.

Let’s try it out!

These two definitions can be used to know what the fractional part of a negative number is:

The result you would expect from {-4.8} is probably -0.8 or 0.8, but we’ve just seen that it is actually 0.2, which is 1-0.8. This means that we can also write the fractional part of a **negative number** as

Keep in mind that I am showing you these other ways to write {x} for the sake of curiosity. The only definition you must remember is the first one.

A few more examples:

What if you want to know the fractional part of a fraction? A fraction is a division after all, so just write the result and then take the fractional part of it.

And that’s all! I hope you liked this post and if something is not clear let me know in the comments!

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