It is really easy to convert fractions to percentages, especially if you use a calculator. On this page, I’ll show you how to convert fractions to percentages with step-by-step instructions and examples.
If you need to know how to convert percentages to fractions or how to convert percentages to decimals, check out the linked pages.
How to Convert Decimals to Percentages
- Multiply the decimal by 100.
- Write your answer with a percentage sign and check if it is reasonable.
Examples
Convert this decimal to a percentage: \[\frac{3}{4}\]
What is the decimal form of \(\frac{3}{4}\)?
I need to divide the numerator by the denominator to convert the fraction to a decimal.
\[3 \div 4 = 0.75\]
What is the product of 0.75 and 100?
\[0.75 \times 100 = 75\]
Is it reasonable that \(\frac{3}{4}=75\%\)?
Yes, it is reasonable that they are equivalent because \(\frac{3}{4}\) is between a half and a whole and \(75\%\) is between \(50\%\) and \(100\%\).
\[\frac{3}{4}=75\%\]
Convert this decimal to a percentage: \[\frac{9}{5}\]
What is the decimal form of \(\frac{9}{5}\)?
I need to divide the numerator by the denominator to convert the fraction to a decimal.
\[9 \div 5 = 1.8\]
What is the product of 1.8 and 100?
\[1.8 \times 100 = 180\]
Is it reasonable that \(\frac{9}{5}=180\%\)?
Yes, it is reasonable that they are equivalent because \(\frac{9}{5}\) is an improper fraction that is just a little bit less than 2 wholes and \(180\%\) is just a little bit less than \(200\%\).
\[\frac{9}{5}=180\%\]
Convert this decimal to a percentage: \[\frac{5}{11}\]
What is the decimal form of \(\frac{5}{11}\)?
I need to divide the numerator by the denominator to convert the fraction to a decimal.
\[5 \div 11 = 0.45454545…\]
If I want to, I can write the repeating decimal with a vinculum over the repeating digits.
\[0.45454545…=0.\overline{45}\]
What is the product of \(0.\overline{45}\) and 100?
\[0.\overline{45} \times 100= 45.454545…\]
Is it reasonable that \(\frac{5}{11}=45.\overline{45}\%\)?
Yes, it is reasonable that they are equivalent because \(\frac{5}{11}\) is just a little bit less than a half and \(45.\overline{45}\%\) is just a little less than \(50\%\).
\[\frac{5}{11}=45.\overline{45}\%\]
How to Multiply by 100 in Your Head
When you convert fractions to percentages, the second step is to multiply the decimal form of the fraction by 100.
You can do this by hand or with a calculator, but there is a really easy way to do it in your head. As I explain in more detail on this page, multiplying by 100 basically increases the entire number by 2 place values.
So, you can multiply any decimal by 100 in your head by moving the decimal to the right two place values.
\[0.25 \times 100 = 25\]
\[0.04 \times 100 = 4\]
\[1.5 \times 100 = 150\]
\[0.678 \times 100 = 67.8\]
\[0.\overline{3} \times 100 = 33.\overline{3}\]
\[0.\overline{27} \times 100 = 27.\overline{27}\]
Why It Works
Fractions and decimals are both methods that we use to represent parts of a whole.
Decimals represent wholes that have been split up into tenths, hundredths, thousandths, ten-thousandths, etc. Fractions represent wholes that have been split up into as many pieces as the denominator says.
The word “percent” literally means “per hundred” or “out of one hundred”.
Decimals reference 1 whole while So, \(75\%\) means “75 out of 100”.
Fractions and decimals
This page explains why we can divide the numerator by the denominator to convert fractions to decimals.
