# What is 1.415 as a fraction?

Looking to convert 1.415 to a fraction? If so, you're in the right place! In this step-by-step guide, we'll show you exactly what the fractional form of 1.415 is and show you exactly how to calculate it so you can convert any decimal number to a fraction. Let's go!

Want to quickly learn or show students how to convert 1.415 to a fraction? Play this very quick and fun video now!

There are many reasons why you might want to convert a decimal to a fraction. The most common reason is because your teacher told you to! But beyond that, the decimal form of a fraction makes it very easy to compare two fractions quickly without having to think about it.

A quick fraction recap here before we begin. The number above the fraction line is the numerator, and the number below the fraction line is the denominator. If you've done much work with fractions you probably already know that, but it never hurts to double check!

Okay, so the first thing to do here is show you that **any number** can be a fraction if you use a 1 as the denominator. Take a look:

What we really want to do though, is get rid of the decimal places completely so that the numerator in our fraction is a whole number. To do this, we have to count the numbers after the decimal point, which in this case is 415.

To get a whole fraction we need to multiply both the numerator and the denominator by 10 if there is one number after the decimal point, 100 if there are two numbers, 1,000 if it's three numbers and 10,000 if it's...well, you get the idea!

In our case 415 is 3 digits long so we need to multiply the numerator and denominator by 1000.

Now we just need to do that multiplication to get our whole fraction:

The next step is to simplify this fraction and, to do that, we need to find the greatest common factor (GCF). This is sometimes also known as:

- Greatest Common Divisor (GCD)
- Highest Common Factor (HCF)
- Greatest Common Denominator (GCD)

The GCF can be a bit complicated to work out by hand but you can use our handy GCF calculator to figure it out.

In the case of 1415 and 1000, the greatest common divisor is 5. This means that to simplify the fraction we can divide by the numerator and the denominator by 5 and we get:

And there you have it! In just a few short steps we have figured out what 1.415 is as a fraction. The complete answer for your enjoyment is below:

1 83/200

*Note: because 1415 is greater than 1000 we have simplified this fraction even further to a mixed fraction.*

Hopefully this tutorial has helped you to understand how to convert a decimal number into a fraction. You can now go forth and convert decimals to fractions as much as your little heart desires!

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