Decimals and Fractions

We hope that our website will answer your decimal and fraction questions while helping you learn how to convert decimals to fractions.

How to Convert a Decimal to a Fraction

To convert a decimal to a fraction take the decimal number removing the decimal separator and leading zeros and place it over 10 to the power of the number of digits to the right of a decimal separator.

Yes, this sounds complicated, but with a couple of examples you’ll see that it’s not. Let’s try to turn .375 into a fraction:

1. Place 0.375 over 1. You can turn any number into a fraction by doing this.
   0.375 1
2. Multiply both the numerator and denominator by 1000. Since 0.375 has tree digits to the right of the decimal point, you need to multiply by 10³ (1000) to get rid of the decimal places.
   0.375 1

   ×

   1000 1000

   =

   375 1000
3. Sometimes this is enough, but in our case the resulting fraction can be reduced further. Divide 375 and 1000 by their Greatest Common Divisor, which is 125.
   375 ÷ 125 1000 ÷ 125
4. Finally, we get the result: 3/8 which since it cannot be reduced any further is a fraction in lowest terms.
   .375

   =

   3 8

For a second example, let’s convert 1.5 to a fraction:

1. Just like in the first example, place 1.5 over 1.
   1.5 1
2. Multiply the numerator and denominator of this new fraction by 10. Why 10? There is only one digit to the right of the decimal separator, so 10 to the power of 1 (10¹) is still 10.
   1.5 1

   ×

   10 10

   =

   15 10
3. It looks like this fraction can be reduced. So divide 15 and 10 by their Greatest Common Divisor, which is 5.
   15 ÷ 5 10 ÷ 5
4. The result, 3/2 is a fraction in simplest terms, but because the numerator, 3 is greater than the denominator, 2, we are looking at an improper fraction. In other words, we can also write it as a mixed number 1 1/2.
   1.5

   =

   3 2

   =

   1

   1 2

What Is a Fraction?

A fraction is a number in the form of a quotient which is produced when dividing a numerator by a denominator. On this website, we are mostly using simple fractions. These are fractions in which both the numerator and denominator are integers. A visual explanation of what a fractions is, can be seen in the figure below:

What Is a Decimal?

A decimal is a number represented in the decimal numeral system. On this website, we are usually referring to decimal fractions when we mention decimals. This type of decimals are rational numbers which have a finite number of non-zero digits after the decimal point.