Decimal to fraction

Simply convert a decimalage to a fraction with this decimal to fraction calculator. Enter a decimalage and click the "calculate fraction" button.

Decimal to fraction calculator

Fraction to decimal Decimal to fraction

Work and steps decimal to fraction

The decimal to fraction calculator has not performed a calculation yet. Please submit the decimalage you want to convert to as fraction. We will show you a step-by-step explanation here.

General explanation decimal to fraction

To convert a decimal to a fraction, follow the steps below.

Example:

0.64

Determine denominator, count digits after decimal seperator

The the number of digits in the decimal after the decimal seperator determines the denominator of the fraction. The denominator of your fraction is the number 1 with the number of digits after the decimal seperator as 0 after it. In this case, the decimal 0.64 has 2 digits after the decimal seperator. Our denominator therefore will be the number 1 with 2 zero's: 100. This process is also calles identifying place value, which means determining the position or location of a digit within a number and understanding its value based on the powers of 10. In the decimal system (base 10), the position of each digit is a power of 10.

Determine the numerator

The numerator of our fraction is nothing more than our decimal value without the decimal seperator. When the value starts with a zero (is less than 1 and greater than than -1), we ignore this zero. So in this case our numerator is 064 = 64 (ignoring the first zero).

Write the decimal as a fraction

Now we have determined our numerator and denominator, we can rewrite the decimal as a fraction.

0.64

100

Reduce fraction if possible

Now we have a fraction, we reduce the fraction to its simplest form. In this case we can divide both numerator and denominator by 4 (which is the greatest common factor).

64 / 4

100 / 4

Decimals vs fractions

Decimals and fractions are two different ways of representing the same concept – parts of a whole or a ratio of two numbers. The relationship between decimals and fractions is such that you can convert one form to the other. They are are interchangeable. You can convert a decimal to a fraction by identifying the place value, and you can convert a fraction to a decimal by dividing the numerator by the denominator. The process may involve simplifying the fraction or using decimal places, depending on the situation.

Example:

4.32

is the same as

Convert decimal to fraction

To convert a decimal number to a fraction, you remove the decimal seperator to get the numerator of the fraction. The denominator of the fraction is determined by counting the digits after the decimal seperator (identify the place value). The denominator is 1 followed by this count in zeros.

This process written as a formula:

Let d be the decimal number (without the decimal seperator), and n be the number of decimal places.

Fraction

10ⁿ

4.32

432

10²

432

100

When the numerator and denominator have a common factor, you can reduce the fraction to its simplest form.