How to Convert Fractions to Decimals and Percentages
Instantly convert any complex fraction into a perfectly rounded decimal using our Fraction to Decimal Converter, or read on to review the manual long-division math rules.
While fractions (like 1/3) are perfect for representing exact mathematical values, they are very difficult to use when dealing with money or the metric system. Decimals and percentages are the standard language of global commerce and science.
Converting a fraction to a decimal requires understanding that a fraction is actually just a division problem waiting to be solved.
The Core Rule: Divide the Top by the Bottom
A fraction consists of two parts: the Numerator (top) and the Denominator (bottom). The line separating them is literally a division symbol.
To convert any fraction to a decimal, simply divide the numerator by the denominator.
Example 1: The Simple Conversion
Convert 3/4 to a decimal.
- Set up the division problem:
3 ÷ 4 - Because 4 is larger than 3, the answer will be less than 1.
3.00 ÷ 4 = 0.75
Converting the Decimal to a Percentage
Once you have the decimal, finding the percentage takes one second. Simply multiply the decimal by 100 (which is the same as moving the decimal point two places to the right) and add a percent sign.
0.75 × 100 = 75%
Terminating vs. Repeating Decimals
When you divide the top by the bottom, the resulting decimal will always fall into one of two categories: terminating or repeating.
1. Terminating Decimals: The division problem eventually ends with a remainder of zero. The decimal is exact.
1/8 = 1 ÷ 8 = 0.125(Terminating)
2. Repeating Decimals: The division problem never ends. A specific sequence of numbers will repeat infinitely.
1/3 = 1 ÷ 3 = 0.333333...(Repeating)1/7 = 1 ÷ 7 = 0.142857142857...(Repeating)
In mathematics, you indicate a repeating decimal by drawing a horizontal line (called a vinculum) over the specific digits that repeat.
The "Denominator of 10, 100, or 1000" Shortcut
If you don't have a calculator and want to avoid long division, you can use a mathematical shortcut if the denominator is easily multipliable to 10, 100, or 1,000.
Because our decimal system is Base-10, any fraction with a denominator of 100 is incredibly easy to convert.
Example: Convert 2/5 to a decimal without long division.
- Find a multiplier to turn the denominator (5) into 10. The multiplier is 2.
- Multiply the top and bottom of the fraction by 2.
(2 × 2) / (5 × 2) = 4/10- Four tenths is written as
0.4.
Example: Convert 7/20 to a decimal.
- Turn the 20 into 100. The multiplier is 5.
(7 × 5) / (20 × 5) = 35/100- Thirty-five hundredths is written as
0.35.
FAQ
What is an Irrational Number? Fractions, by definition, always result in either terminating or repeating decimals (these are called Rational Numbers). An Irrational Number is a decimal that goes on forever without ever repeating a pattern. The most famous example is Pi (3.14159265...). Because it is irrational, Pi cannot be written as a perfect fraction.
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