Convert 10.875 to a fraction

Decimal to Fraction Calculator

Result: 10.875 as a fraction = 87/8 or 10875/1000

How to convert 10.875 to a fraction?

Step 1

The first step of converting any decimal to a fraction is to write it as a fraction.

Put the decimal value as the numerator (the number at the top) and 1 as the denominator (the number at the bottom). No matter what the decimal number is, we always use 1 as the denominator.

10.875 as 10.875/1

Step 2

We now multiply both the numerator and the denominator by the power of 10 for every digit there is after the decimal point. We can write this as:

10.875/1 = 10.875 x 1000/1 x 1000 = 10875/1000

Step 3

Reduce the fraction into its simplest form, which is when the numerator and denominator cannot be any smaller.

We work out the simplest form by finding the Greatest Common Factor (GCF). A factor is a number that will divide into another without remainder, and the Greatest Common Factor is the largest number that is a factor of two or more numbers.

What we need to do is find the GCF of 10875 and 1000.

The factors of 10875 are: 1, 3, 5, 15, 25, 29, 75, 87, 125, 145, 375, 435, 725, 2175, 3625, 10875

The factors of 1000 are: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000

If we look at the two sets of numbers we’ve listed, the Greatest Common Factor for both 10875 and 1000 is: 125

So to reduce the fraction we divide 10875 and 1000 by 125.

10875/1000 = 10875 ÷ 125/1000 ÷ 125 = 87/8

Therefore, 10.875 as a fraction = 87/8 or 10875/1000