As a Fraction [Decimal to Fraction Calculator]

With the convenience of the decimal to fraction calculator aside, let’s not forget the importance of being able to manually convert decimal to fraction on paper.

Terminating decimals have a limited number of digits after the decimal point. Follow these steps to manually convert any terminating decimal into a fraction:

Step a: Write the decimal number in fraction format, with the number as the numerator and 1 in the denominator.

Step b: Now, multiply the numerator and the denominator by 10 for every digit left of the decimal point.

Step c: Next, reduce the fraction into its simplest form.

Terminating Decimal to Fraction Example: 6775.21 = 6775 ²¹/₁₀₀

Non-Terminating Decimals (recurring)

Non-terminating also known as recurring decimals are those decimals which have one or more repeating digits after the decimal point which continue on infinitely. Non-terminating decimals are typically more complex to manually convert into fractions. Next we'll explain the steps involved.

Let us find the value of decimal 0.4444... in fraction form.

Step 1: Take the repeating decimal you are trying to convert as x. Let x be equal to 0.44444….

Step 2: Multiply the value of X by the power of 10, such that the resulting number has the same number on the right side of the decimal.

Hence, 10x = 4.44444….

Step 3: Subtact the output of the the first two steps

10x-x = 4.444444...-0.4444444….

9x= 4

= 4/9

Step 4: Resulting in a fraction number of the decimal number.

x=4/9

Recurring Decimal to Fraction Example:

5605.6666 = 5605 ⁶⁶⁶⁶/₁₀₀₀₀ = ⁶⁶⁶/₁₀₀₀ = ⁶⁶/₁₀₀ = ²/₃ (rounded)

Irrational Decimals

Irrational decimals go on forever and never form a repeating pattern. This type of decimal cannot be expressed as a fraction.

Irrational Decimal Example: 0.475759271.....

Common questions on Decimals and Fractions

What are whole numbers?

Whole numbers are numbers 0, 1, 2, 3, etc. Whole numbers do not have a decimal point or fractional part. Whole numbers are always positive. Negative numbers are not considered whole.

What are mixed numbers?

A mixed number is made up of a whole number and a proper fraction.

What are proper fractions?

Fractions where the numerator (the top number) is less than the denominator (the bottom number). Example ²/₃

What are improper fractions?

Fractions where the numerator (the top number) is greater than or equal to the denominator (the bottom number). Example ³/₂

What are simple or reduced fractions?

Fractions whose top number (numerator) and bottom number (denominator) cannot be any smaller, while still being a whole number. That is to say, the number can no longer be divided by any number other than one while still being a whole number. ¹/₃ is a good example of a fully reduced fraction.

What are imperial fractions?

Yards, feet and inches are part all part of the Imperial measurement system so a quarter of an inch ¹/₄ is described as an Imperial fraction.

What does the Greatest Common Factor (GCF) mean?

The greatest common factor is also referred to as the highest common factor. In math this refers to the greatest common divisor of two or more whole numbers (also known as integers). In simple terms this is the biggest number that can divide even into two or more numbers. For example the GCF for 4 and 8 is 4. Use our Decimal to Fraction calculator for a break down of the factors and GCF value between numbers.

Why is there a need to convert decimals to fractions anyway?

The U.S. is one of a few countries world wide which still uses the Imperial system of measurement, which is a fractional measurement system, where items are measured in feet, inches, pounds, ounces, yards, and so on. With the majority of the rest of the world using the metric system, which is a decimal measurement system, where items are measured in cm, metres, grams, kilos, and so on.