Fraction to Decimal

Welcome to fraction to decimal, our article about converting fractions to decimals. We start with a few definitions, and then explain in detail how to convert fractions to decimals, along with examples. Here you can learn how to change simple, mixed, proper and improper fractions to decimals, either repeating or terminating. Read on to learn all about turning fractions into decimals and make sure to check out our fraction to decimal converter further down on this page.

What is a Fraction

In math, a fraction is a quotient of numbers; the numerator divided by the denominator.

Throughout this article we assume \hspace{3px}n, p, q \hspace{3px}\epsilon\hspace{3px}\mathbb{Z},\hspace{3px} q\neq 0:

As simple fraction is made of two integers p/q; e.g. 1/4, 6/3 and -3/8
A proper fraction is made of two integers p/q with p < q, e.g. 2/3
An improper fraction is made of two integers p/q with p ≥ q, e.g. 3/2 and 4/4
A mixed fraction or mixed number is the sum of a (non-zero) integer n and a proper fraction in the form n + p/q, e.g. 1 1/2

From the definitions above we can conclude that

  • a simple fraction can be positive, neutral when p=0, or negative, proper, or improper
  • the absolute value |p/q| of a proper fraction is < 1, that is -1 < p/q < 1
  • the absolute value |p/q| of an improper fraction is ≥ 1, that is p/q ≤ -1 and p/q ≥ 1
  • a mixed fraction n + p/q can be changed to an improper fraction (nq + p)/q and vice versa

What is a Decimal Fraction

A decimal fraction like 3/10, 17/100 or 113/1000 is a fraction of the form p/q where the denominator q is a power of ten, such as 10 = 101, 100 = 102, 1000 = 103, and so on.

Convert Fraction to Decimal

To convert a simple fraction to decimal divide the numerator by the denominator using a calculator. For example: 7/8 = 0.875, a terminating decimal.

Note that you can easily convert fractions to decimals without a calculator if you change the denominator into a power of 10, that is if you convert it to a decimal fraction.

For example, by multiplying 7/8 by 125 we get 875/1000. For each zero of the power of 10 you simply move the decimal point of the nominator one place to the left from the last digit.

In 875/1000 the denominator has three zeroes, so we get 0.875 by moving the decimal point three digits to the left of the 5 in 875: 875 → 0.875.

If you see some digits or a pattern of digits repeating indefinitely, such as in the case when you change 5/6 to decimal, then you can use the overline syntax 0.83 to denote 0.8333....

Alternatively, you can write 0.8(3) to denote a non-terminating, but repeating decimal like 0.83. More information about terminating and repeating decimals can be found on our home page.

To convert a mixed fraction to decimal, first change the mixed number to an improper fraction using n + p/q = (nq + p) / q. For example, 3 1/4 = (3x4 + 1)/4 = 13/4.

Then proceed as explained above to get 13/4 = 3.25. Keep n + p/q = (nq + p) / q in mind for converting mixed fractions to improper fractions.

Instead of using a calculator, both, simple fractions as well as mixed fraction can also be converted to decimal notation by means of the long division method.

Fraction to Decimal Converter

Our fraction to decimal converter can handle all kind of fractions, simple and mixed, proper as well as improper. Just enter the fraction you want to convert to a decimal, then hit the convert button. For example, enter 1/8, -3 1/2 or 4 2/3.


In Decimal:

If the decimal is non-terminating and repeating, then the repeating pattern is given in parenthesis (). For example, for 4 2/3 you will see 4.(6). That essentially means 4.6 = 4.66666666666...

Bookmark our fraction to decimal converter now!

Note that you can also find many fraction to decimal conversations using the search button in the sidebar. Here you can find decimal to fraction, the inverse operation of what this page has been about.

This brings us to the end of our article fractions into decimals. By reading all of the above you can convert all kind of fractions to decimals and you also know where to find a fraction calculator with whole numbers.

We sum our article up as follows:

Fraction to Decimal

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More Information:

Fraction (mathematics) on Wikipedia

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