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Fractions as Decimals

Dividing the denominator into the numerator

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Fractions as Decimals
License: CC BY-NC 3.0

Michelle and Terry are shooting hoops. Michelle made 7 out of the last 10 shots. Terry made 6 out the last 8 shots. Compare their results using decimals. Who had better results?

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

Converting Fractions to Decimals

Decimals and fractions both represent quantities that are part of a whole. Fractions can also be converted to a decimal number. There are two ways to convert a fraction to a decimal.

The first way is to think in terms of place value. If a fraction that has ten as a denominator, you can think of that fraction as tenths. Here is a fraction of a tenth and the decimal equivalent.

\begin{align*}\frac{6}{10}=.6\end{align*}

There is one decimal place in tenths, so this decimal is accurate. This is a very useful method when the denominator is a base ten value like: \begin{align*}10, 100, 1,000 \ldots\end{align*}

Here is a fraction with a base ten value of 1,000.

\begin{align*}\frac{125}{1000}\end{align*}

There are three decimal places in a thousandth decimal. There are three digits in the numerator. This fraction converts easily to a decimal.

\begin{align*}\frac{125}{1000}=0.125\end{align*}

The second way is to use division. The fraction bar is also a symbol for division. The numerator is the dividend and the denominator is the divisor.

Here is another fraction.

\begin{align*}\frac{3}{5}\end{align*}

To change \begin{align*}\frac{3}{5}\end{align*} to a decimal number, divide 3 by 5.  Remember that you are looking for a decimal number. Use zero placeholders to help find the decimal value.

\begin{align*}\begin{array}{rcl} && \overset{ \ \ \ 0.6}{5 \overline{ ) {3.0 \;}}}\\ && \underline{- \; 3.0}\\ && \quad \ \ 0 \end{array}\end{align*}

The decimal value of \begin{align*}\frac{3}{5}\end{align*} is \begin{align*}0.6\end{align*}.

Examples

Example 1

Earlier, you were given a problem about Michelle and Terry playing basketball.

Michelle made 7 out of the last 10 shots and Terry made 6 out the last 8 shots. 7 out of 10 is also \begin{align*}\frac{7}{10}\end{align*}. 6 out of 8 is also \begin{align*}\frac{6}{8}\end{align*}. Convert the fractions to decimals and compare their results.

First, convert \begin{align*}\frac{7}{10}\end{align*} to a decimal. The denominator is a base ten number.

\begin{align*}\frac{7}{10}=0.7\end{align*}

Then, convert \begin{align*}\frac{6}{8}\end{align*} to a decimal. Divide 6 by 8.

\begin{align*}\begin{array}{rcl} && \overset{ \ \ \ 0.75}{8 \overline{ ) {6.00}}}\\ && \underline{ \;-56}\\ && \quad \ \ 40 \\ && \ \ \ \underline{-40} \\ && \qquad 0 \end{array}\end{align*}

Next, compare the decimals. The better player has the larger decimal number.

\begin{align*}0.7 < 0.75\end{align*}

Terry made more of his shots than Michelle.

Example 2

Write the following fraction as a decimal.

\begin{align*}\frac{1}{4}\end{align*}

One way is to use base ten values. First, find an equivalent fraction of \begin{align*}\frac{1}{4}\end{align*} with a denominator of 100.

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

Then, convert the fraction to a decimal. \begin{align*}\frac{25}{100}\end{align*} is also 25 hundredths.

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

The decimal value of \begin{align*}\frac{1}{4}\end{align*} is 0.25.

The other way is to use division. Divide 1 by 4. Use zero place holders if needed.

\begin{align*}\begin{array}{rcl} && \overset{ \quad 0.25}{4 \overline{ ) {1.00 \;}}}\\ && \ \ \ \underline{-8}\\ && \quad \ \ 20 \\ && \ \ \ \underline{-20} \\ && \qquad 0 \end{array}\end{align*}

The decimal value of \begin{align*}\frac{1}{4}\end{align*} is 0.25.

Example 3

Convert the fraction to a decimal.

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

This fraction has a base ten value in the denominator. Place the 8 in the tenth place.

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

The decimal value of \begin{align*}\frac{8}{10}\end{align*} is \begin{align*}0.8\end{align*}.

Example 4

Convert the fraction to a decimal.

\begin{align*}\frac{5}{100}\end{align*}

This fraction has a base ten value in the denominator. Place 5 in the hundredths place.

\begin{align*}\frac{5}{100}=0.05\end{align*}

The decimal value of \begin{align*}\frac{5}{100}\end{align*} is \begin{align*}0.05\end{align*}.

Example 5

Convert the fraction to a decimal.

 \begin{align*}\frac{4}{5}\end{align*}

Divide the numerator by the denominator. Use zero placeholders if needed.

\begin{align*}\begin{array}{rcl} && \overset{ \quad 0.8}{5 \overline{ ) {4.0}}}\\ && \underline{- \; 4.0}\\ && \quad \ \ 0 \end{array}\end{align*}

The decimal value of \begin{align*}\frac{4}{5}\end{align*} is \begin{align*}0.8\end{align*}.

Review

Convert the following fractions as decimals.

  1.  \begin{align*}\frac{3}{10}\end{align*} 
  2. \begin{align*}\frac{23}{100}\end{align*}
  3. \begin{align*}\frac{9}{100}\end{align*}
  4. \begin{align*}\frac{8}{10}\end{align*}
  5. \begin{align*}\frac{182}{1000}\end{align*}
  6. \begin{align*}\frac{25}{100}\end{align*}
  7. \begin{align*}\frac{6}{10}\end{align*}
  8. \begin{align*}\frac{125}{1000}\end{align*}
  9. \begin{align*}\frac{1}{10}\end{align*}
  10. \begin{align*}\frac{2}{100}\end{align*}
  11. \begin{align*}\frac{1}{2}\end{align*}
  12. \begin{align*}\frac{1}{4}\end{align*}
  13. \begin{align*}\frac{3}{4}\end{align*}
  14. \begin{align*}\frac{3}{6}\end{align*} 
  15. \begin{align*}\frac{3}{5}\end{align*} 

Review (Answers)

To see the Review answers, open this PDF file and look for section 5.19.

Resources 

 

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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).

Equivalent

Equivalent means equal in value or meaning.

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.

Irrational Number

An irrational number is a number that can not be expressed exactly as the quotient of two integers.

Place Value

The value of given a digit in a multi-digit number that is indicated by the place or position of the digit.

Image Attributions

  1. [1]^ License: CC BY-NC 3.0

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