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Decimals as Fractions

Fractions with 10, 100 or 1000 as denominators

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Decimals as Fractions
License: CC BY-NC 3.0

About 0.71 of the surface of the Earth is covered with water. That means 0.29 of the Earth's surface is land. What fraction of the surface of the Earth is water? What fraction of the Earth's surface is land?

In this concept, you will learn to convert decimals to fractions.

Converting Decimals to Fractions

Decimals and fractions are related. They both represent a part of a whole. With a decimal, the part of a whole is written using a decimal point. With a fraction, the part of a whole is written using a fraction bar and has a numerator and a denominator. Because fractions and decimals are related, decimals can be written as fractions. Use the place value of the decimal to convert it to a fraction.

Here is a decimal number.

0.67

The chart represents the place value of the decimal number.

Tens Ones Decimal Point Tenths Hundredths Thousandths Ten-Thousandths
. 6 7

The fraction is described by reading the decimal, “sixty-seven hundredths.” The numerator is 67 and the denominator is 100. The place value of the decimal number will indicate the denominator of the fraction.

\begin{align*}0.67 = \frac{67}{100}\end{align*}

Here is another decimal number

0.5

Tens Ones Decimal Point Tenths Hundredths Thousandths Ten-Thousandths
. 5

Convert this decimal number to a fraction.

This decimal number is read as “five tenths.” The numerator is the five and the denominator is the place value of tenths.

\begin{align*}0.5 = \frac{5}{10}\end{align*}

You can simplify the fraction. The greatest common factor (GCF) of 5 and 10 is 5.

\begin{align*}\frac{5}{10} = \frac{1}{2}\end{align*}

0.5 is written as \begin{align*}\frac{5}{10}\end{align*} or \begin{align*}\frac{1}{2}\end{align*}.

Examples

Example 1

Earlier, you were given a problem about the Earth’s water and land.

About 0.71 of the entire Earth is water and 0.29 of the Earth is land. Convert the decimals to fractions to find the fraction of the Earth that is water and land.

First, convert the decimal 0.71 to a fraction. 0.71 is 71 hundredths.

\begin{align*}0.71 = \frac{71}{100}\end{align*}

71 is a prime number and cannot be simplified.

Then, convert the decimal 0.29 to a fraction. 0.29 is 29 hundredths.

\begin{align*}0.29 = \frac{29}{100}\end{align*}

29 is also a prime number and cannot be simplified.

The Earth is \begin{align*}\frac{71}{100}\end{align*} water and \begin{align*}\frac{29}{100}\end{align*} land.

Example 2

Jessie has completed 0.85 of her homework. If she was going to express this number as a fraction what would the fraction be? Write your answer in simplest form.

First, convert the decimal number to a fraction. 0.85 is eighty-five hundredths. The numerator is 85 and the denominator is 100.

\begin{align*}\frac{85}{100}\end{align*}

Then, simplify thefraction. The greatest common factor of 85 and 100 is 5.

\begin{align*}\frac{85}{100} = \frac{17}{20}\end{align*}

0.85 is written as \begin{align*}\frac{17}{20}\end{align*}.

Example 3

Convert the decimal number to a fraction in simplest form.

0.8

First, convert the decimal to a fraction. 0.8 is 8 tenths.

\begin{align*}0.8 = \frac{8}{10}\end{align*}

Then, simplify the fraction. The GCF of 8 and 10 is 2.

\begin{align*}\frac{8}{10} = \frac{4}{5}\end{align*}

0.8 is written as \begin{align*}\frac{4}{5}\end{align*} in simplest form.

Example 4

Convert the decimal number to a fraction in simplest form.

0.25

First, convert the decimal to a fraction. 0.25 is 25 hundredths.

\begin{align*}0.25 = \frac{25}{100}\end{align*}

Then, simplify the fraction. The GCF of 25 and 100 is 25.

\begin{align*}\frac{25}{100} = \frac{1}{4}\end{align*}

0.25 is written as \begin{align*}\frac{1}{4}\end{align*} in simplest form.

Example 5

Convert the decimal number to a fraction in simplest form.

0.75

First, convert the decimal to a fraction. 0.75 is 75 hundredths.

\begin{align*}0.75 = \frac{75}{100}\end{align*}

Then, simplify the fraction. The GCF of 75 and 100 is 25.

\begin{align*}\frac{75}{100} = \frac{3}{4}\end{align*}

0.75 is written as \begin{align*}\frac{3}{4}\end{align*} in simplest form.

Review

Write each decimal as a fraction. Do not simplify.

  1. 0.67
  2. 0.33
  3. 0.45
  4. 0.27
  5. 0.56
  6. 0.7
  7. 0.98
  8. 0.32
  9. 0.04
  10. 0.07
  11. 0.056
  12. 0.897
  13. 0.372
  14. 0.652
  15. 0.032

Review (Answers)

To see the Review answers, open this PDF file and look for section 5.17.

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Vocabulary

Decimal

In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).

fraction

A fraction is a part of a whole. A fraction is written mathematically as one value on top of another, separated by a fraction bar. It is also called a rational number.

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