Decimal to Fraction


Before we start talking about decimal to fraction conversion, let’s say something about decimals.

Well, decimal numbers, or as we shorter call them decimals, are a special form of fractions. As classic fractions, they are the way to represent "not-whole" numbers.

In decimals we operate with a system based on 10s. They are much easier than regular fractions. And they have a different way of noting.

Percents, on the other hand, are even more specific fractions. They are fractions with the denominator = 100.

OK, let’s see and convert decimal to fraction in the following less-than-one example, with just one decimal place.

0.8 = 8 ÷2 =   4  
10 ÷2   5  

So, no whole numbers, just 8 10ths. Afterwards we can reduce of course.

Now let’s see a greater-than-one example again with 1 decimal place.

. =

2.3 = 2

3 = 2×10 + 3 = 23
10 10 10

A point (dot) is a separation point between whole numbers part on the left and the fractions part (10ths, 100ths, 1000ths etc) on the right hand side.

This example, 2 wholes and 3/10, is represented by 2.3.

We notice that there are no 10ths stated anywhere. That’s because they are already implied.

Here’s a shorter (recommended) version for this conversion:

Decimal to Fraction Conversion 1 place

Only 1 decimal place (digit) – means we’re dealing with 10ths, so 1 zero in the denominator (apart from mandatory 1), and then you just lift the whole number (number 4 in this case) up to the numerator.

Now with 2 decimal places:

Decimal to Fraction Conversion 2 places

Again, very similar, we have 2 decimal places – that means we’ll have 2 zeros in our denominator. At the end – we lift up the whole number and join it with decimal/fraction part.

It doesn’t matter how big the number is – you always follow the same pattern.

Let’s demonstrate it one more time, now a 2 digit number with 3 decimal places:

Decimal to Fraction Conversion 3 places

After this fast conversion, we simplify if applicable.

for Decimal to Fraction Conversion page:

  • First we deal with fraction part, and then with a whole numbers part

  • How many decimal places – that many zeros in the denominator

  • After the fraction part – we lift the whole number part (if any) up to the numerator

  • Due to 10 based numbers as denominators – we can only simplify by 10s and its factors, i.e. 5 and 2

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