Fractions Vs Decimals

Converting between percents, fractions, & decimals

For example, learn how 50%, 1/2, and 0.5 are all equivalent.

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Percents, fractions, and decimals are all just different ways of writing numbers. For example, each of the following are equivalent:

Percent Fraction Decimal

50\%50%50, percent \dfrac{1}{2}

2

1

start fraction, 1, divided by, 2, end fraction 0.50.50, point, 5

In conversation, we might say Ben ate 50\%50%50, percent of the pizza, or \dfrac12

2

1

start fraction, 1, divided by, 2, end fraction of the pizza, or 0.50.50, point, 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

The key here is to turn \dfrac35

5

3

start fraction, 3, divided by, 5, end fraction to a fraction with a denominator of 100100100. To do this, we need to know what times 555 gives us 100100100:

5 \times \,\blueD? = 1005×?=1005, times, space, start color blueD, question mark, end color blueD, equals, 100

The number is 100 \div 5 = \blueD{20}100÷5=20100, divided by, 5, equals, start color blueD, 20, end color blueD:

5 \times \blueD{20} = 1005×20=1005, times, start color blueD, 20, end color blueD, equals, 100

Now we're ready to convert \dfrac35

5

3

start fraction, 3, divided by, 5, end fraction to 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}}}

Google Classroom

Facebook

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Percents, fractions, and decimals are all just different ways of writing numbers. For example, each of the following are equivalent:

Percent Fraction Decimal

50\%50%50, percent \dfrac{1}{2}

2

1

start fraction, 1, divided by, 2, end fraction 0.50.50, point, 5

In conversation, we might say Ben ate 50\%50%50, percent of the pizza, or \dfrac12

2

1

start fraction, 1, divided by, 2, end fraction of the pizza, or 0.50.50, point, 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%15, percent to a simplified fraction.

\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}

15%