# Fractions as Decimals

## Dividing the denominator into the numerator

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Fractions as Decimals

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*}

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

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### Vocabulary Language: English

TermDefinition
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.