Convert 25.6 to a fraction

Decimal to Fraction Calculator

Result: 25.6 as a fraction = 128/5 or 256/10

How to convert 25.6 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.

25.6 as 25.6/1

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:

25.6/1 = 25.6 x 10/1 x 10 = 256/10

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 256 and 10.

The factors of 256 are: 1, 2, 4, 8, 16, 32, 64, 128, 256

The factors of 10 are: 1, 2, 5, 10

If we look at the two sets of numbers we’ve listed, the Greatest Common Factor for both 256 and 10 is: 2

So to reduce the fraction we divide 256 and 10 by 2.

256/10 = 256 ÷ 2/10 ÷ 2 = 128/5

Therefore, 25.6 as a fraction = 128/5 or 256/10