Converting between percents, fractions, & decimals

CCSS Math: 6.RP.A.3, 6.RP.A.3c
For example, learn how 50%, 1/2, and 0.5 are all equivalent.
Percents, fractions, and decimals are all just different ways of writing numbers. For example, each of the following are equivalent:
PercentFractionDecimal
50%50\%12\dfrac{1}{2}0.50.5
In conversation, we might say Ben ate 50%50\% of the pizza, or 12\dfrac12 of the pizza, or 0.50.5 of the pizza. All three of these phrases mean the exact same thing.
In this article, we'll learn how to convert between percents, fractions, and decimals.

Converting between percents and fractions

Percents to fractions

Let's look at an example converting 15%15\% to a simplified fraction.
15%=15100Write the percent as a fraction=15÷5100÷5Divide the top and bottom by 5=320Simplify\begin{aligned} 15\% &= \dfrac{{15}}{100} &\small{\gray{\text{Write the percent as a fraction}}} \\\\\\\\ &= \dfrac{15 \div 5}{100 \div 5} &\small{\gray{\text{Divide the top and bottom by 5}}}\\\\\\\\ &= \dfrac{3}{20} &\small{\gray{\text{Simplify}}} \end{aligned}
We figured out that 15%15\% is equivalent to 320\dfrac3{20}.
Convert 44%44\% to a simplified fraction.
  • Your answer should be
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4

44%=44100Write the percent as a fraction=44÷4100÷4Divide the top and bottom by 4=1125Simplify\begin{aligned} 44\% &= \dfrac{{44}}{100} &\small{\gray{\text{Write the percent as a fraction}}} \\\\\\\\ &= \dfrac{44 \div 4}{100 \div 4} &\small{\gray{\text{Divide the top and bottom by 4}}}\\\\\\\\ &= \dfrac{11}{25} &\small{\gray{\text{Simplify}}} \end{aligned}

Fractions to percents

Let's convert 35\dfrac35 to a percent. The key here is to turn 35\dfrac35 to a fraction with a denominator of 100100. To do this, we need to know what times 55 gives us 100100:
5×?=1005 \times \,\blueD? = 100
The number is 100÷5=20100 \div 5 = \blueD{20}:
5×20=1005 \times \blueD{20} = 100
Now we're ready to convert 35\dfrac35 to a percent:
35=3×205×20Multiply to get a denominator of 100=60100Simplify=60%Write as a percent\begin{aligned} \dfrac35 &= \dfrac{{3 \times \blueD{20}}}{5 \times \blueD{20}} &\small{\gray{\text{Multiply to get a denominator of 100}}} \\\\\\\\ &= \dfrac{60}{100} &\small{\gray{\text{Simplify}}}\\\\\\\\ &= 60\% &\small{\gray{\text{Write as a percent}}} \end{aligned}
We figured out that 35\dfrac35 is equivalent to 60%60\%.
Convert 1225\dfrac{12}{25} to a percent.
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}
%\%

The key here is to turn 1225\dfrac{12}{25} to a fraction with a denominator of 100100. To do this, we need to know what times 2525 gives us 100100:
25×?=10025 \times \,\blueD? = 100
The number is 100÷25=4100 \div 25 = \blueD{4}:
25×4=10025 \times \blueD{4} = 100
Now we're ready to convert 1225\dfrac{12}{25} to a percent:
1225=12×425×4Multiply to get a denominator of 100=48100Simplify=48%Write as a percent\begin{aligned} \dfrac{12}{25} &= \dfrac{{12 \times \blueD{4}}}{25 \times \blueD{4}} &\small{\gray{\text{Multiply to get a denominator of 100}}} \\\\\\\\ &= \dfrac{48}{100} &\small{\gray{\text{Simplify}}}\\\\\\\\ &= 48\% &\small{\gray{\text{Write as a percent}}} \end{aligned}
We figured out that 1225\dfrac{12}{25} is equivalent to 48%48\%.

Converting between percents and decimals

Percents to decimals

Let's convert 8%8\% to a decimal:
8%=8100Write the percent as a fraction=0.088100is 8 hundredths\begin{aligned} 8\% &= \dfrac{{8}}{100} &\small{\gray{\text{Write the percent as a fraction}}} \\\\\\\\ &= 0.08 &\small{\gray{\dfrac{8}{100}\text{is 8 hundredths}}}\end{aligned}
We figured out that 8%8\% is equivalent to 0.080.08.
Convert 4%4\% to a decimal.
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

4%=4100Write the percent as a fraction=0.044100is 4 hundredths\begin{aligned} 4\% &= \dfrac{{4}}{100} &\small{\gray{\text{Write the percent as a fraction}}} \\\\\\\\ &= 0.04 &\small{\gray{\dfrac{4}{100}\text{is 4 hundredths}}}\end{aligned}
Convert 70%70\% to a decimal.
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

70%=70100Write the percent as a fraction=0.7070100is 70 hundredths\begin{aligned} 70\% &= \dfrac{{70}}{100} &\small{\gray{\text{Write the percent as a fraction}}} \\\\\\\\ &= 0.70 &\small{\gray{\dfrac{70}{100}\text{is 70 hundredths}}}\end{aligned}

Decimals to percents

Let's convert 0.050.05 to a percent:
0.05=5100This is 5 hundredths=5%Write as a percent\begin{aligned} 0.05 &= \dfrac{{5}}{100} &\small{\gray{\text{This is 5 hundredths}}} \\\\\\\\ &= 5\% &\small{\gray{\text{Write as a percent}}}\end{aligned}
We figured out that 0.050.05 is equivalent to 5%5\%.
Convert 0.140.14 to a percent.
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}
%\%

0.14=14100This is 14 hundredths=14%Write as a percent\begin{aligned} 0.14 &= \dfrac{{14}}{100} &\small{\gray{\text{This is 14 hundredths}}} \\\\\\\\ &= 14\% &\small{\gray{\text{Write as a percent}}}\end{aligned}
Converting from a decimal to a percent can be tricky when the decimal is in tenths. Let's see if you can figure it out!
Convert 0.30.3 to a percent.
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}
%\%

0.3=310This is 3 tenths=30100This is 30 hundredths=30%Write as a percent\begin{aligned} 0.3 &=\dfrac{{3}}{10} &\small{\gray{\text{This is 3 tenths}}} \\\\\\\\ &=\dfrac{{30}}{100} &\small{\gray{\text{This is 30 hundredths}}} \\\\\\\\ &= 30\% &\small{\gray{\text{Write as a percent}}}\end{aligned}
Convert 0.90.9 to a percent.
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}
%\%

0.9=910This is 9 tenths=90100This is 90 hundredths=90%Write as a percent\begin{aligned} 0.9 &=\dfrac{{9}}{10} &\small{\gray{\text{This is 9 tenths}}} \\\\\\\\ &=\dfrac{{90}}{100} &\small{\gray{\text{This is 90 hundredths}}} \\\\\\\\ &= 90\% &\small{\gray{\text{Write as a percent}}}\end{aligned}

Let's practice!

Convert 0.820.82 to a percent.
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}
%\%

0.82=82100This is 82 hundredths=82%Write as a percent\begin{aligned} 0.82 &= \dfrac{{82}}{100} &\small{\gray{\text{This is 82 hundredths}}} \\\\\\\\ &= 82\% &\small{\gray{\text{Write as a percent}}}\end{aligned}
Convert 9%9\% to a decimal.
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

9%=9100Write the percent as a fraction=0.099100is 9 hundredths\begin{aligned} 9\% &= \dfrac{{9}}{100} &\small{\gray{\text{Write the percent as a fraction}}} \\\\\\\\ &= 0.09 &\small{\gray{\dfrac{9}{100}\text{is 9 hundredths}}}\end{aligned}
Convert 810\dfrac{8}{10} to a percent.
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}
%\%

The key here is to turn 810\dfrac{8}{10} to a fraction with a denominator of 100100. To do this, we need to know what times 1010 gives us 100100:
10×?=10010 \times \,\blueD? = 100
The number is 100÷10=10100 \div 10 = \blueD{10}:
10×10=10010 \times \blueD{10} = 100
Now we're ready to convert 810\dfrac{8}{10} to a percent:
810=8×1010×10Multiply to get a denominator of 100=80100Simplify=80%Write as a percent\begin{aligned} \dfrac{8}{10} &= \dfrac{{8 \times \blueD{10}}}{10 \times \blueD{10}} &\small{\gray{\text{Multiply to get a denominator of 100}}} \\\\\\\\ &= \dfrac{80}{100} &\small{\gray{\text{Simplify}}}\\\\\\\\ &= 80\% &\small{\gray{\text{Write as a percent}}} \end{aligned}
We figured out that 810\dfrac{8}{10} is equivalent to 80%80\%.
Convert 34%34\% to a simplified fraction.
  • Your answer should be
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4

34%=34100Write the percent as a fraction=34÷2100÷2Divide the top and bottom by 2=1750Simplify\begin{aligned} 34\% &= \dfrac{{34}}{100} &\small{\gray{\text{Write the percent as a fraction}}} \\\\\\\\ &= \dfrac{34 \div 2}{100 \div 2} &\small{\gray{\text{Divide the top and bottom by 2}}}\\\\\\\\ &= \dfrac{17}{50} &\small{\gray{\text{Simplify}}} \end{aligned}
Convert 0.40.4 to a percent.
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}
%\%

0.4=410This is 4 tenths=40100This is 40 hundredths=40%Write as a percent\begin{aligned} 0.4 &=\dfrac{{4}}{10} &\small{\gray{\text{This is 4 tenths}}} \\\\\\\\ &=\dfrac{{40}}{100} &\small{\gray{\text{This is 40 hundredths}}} \\\\\\\\ &= 40\% &\small{\gray{\text{Write as a percent}}}\end{aligned}
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