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# Fractions as Decimals

## Dividing the denominator into the numerator

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Fractions as Decimals

Credit: Håkan Dahlström
Source: https://www.flickr.com/photos/dahlstroms/7189993560/

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.

### Guidance

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.

610=.6

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: 10,100,1,000\begin{align*}10, 100, 1,000 \ldots\end{align*}

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

1251000

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

1251000=0.125

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.

35

To change 35\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.

5)3.0¯¯¯¯¯¯   0.63.0  0

The decimal value of 35\begin{align*}\frac{3}{5}\end{align*} is 0.6\begin{align*}0.6\end{align*}.

### Guided Practice

Write the following fraction as a decimal.

14

One way is to use base ten values. First, find an equivalent fraction of 14\begin{align*}\frac{1}{4}\end{align*} with a denominator of 100.

14=25100

Then, convert the fraction to a decimal. 25100\begin{align*}\frac{25}{100}\end{align*} is also 25 hundredths.

25100=0.25

The decimal value of 14\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.

4)1.00¯¯¯¯¯¯¯¯0.25   8  20   200

The decimal value of 14\begin{align*}\frac{1}{4}\end{align*} is 0.25.

### Examples

Convert each fraction to a decimal.

#### Example 1

810

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

810=0.8

The decimal value of 810\begin{align*}\frac{8}{10}\end{align*} is 0.8\begin{align*}0.8\end{align*}.

#### Example 2

5100

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

5100=0.05

The decimal value of 5100\begin{align*}\frac{5}{100}\end{align*} is 0.05\begin{align*}0.05\end{align*}.

#### Example 3

45

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

5)4.0¯¯¯¯¯¯0.84.0  0

The decimal value of 45\begin{align*}\frac{4}{5}\end{align*} is 0.8\begin{align*}0.8\end{align*}.

Credit: Eugene Kim
Source: https://www.flickr.com/photos/eekim/8697169257/

Remember 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 710\begin{align*}\frac{7}{10}\end{align*}. 6 out of 8 is also 68\begin{align*}\frac{6}{8}\end{align*}. Convert the fractions to decimals and compare their results.

First, convert 710\begin{align*}\frac{7}{10}\end{align*} to a decimal. The denominator is a base ten number.

710=0.7

Then, convert 68\begin{align*}\frac{6}{8}\end{align*} to a decimal. Divide 6 by 8.

8)6.00¯¯¯¯¯¯¯   0.7556  40   400

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

0.7<0.75

Terry made more of his shots than Michelle.

### Explore More

Convert the following fractions as decimals.

1.  310\begin{align*}\frac{3}{10}\end{align*}
2. 23100\begin{align*}\frac{23}{100}\end{align*}
3. 9100\begin{align*}\frac{9}{100}\end{align*}
4. 810\begin{align*}\frac{8}{10}\end{align*}
5. 1821000\begin{align*}\frac{182}{1000}\end{align*}
6. 25100\begin{align*}\frac{25}{100}\end{align*}
7. 610\begin{align*}\frac{6}{10}\end{align*}
8. 1251000\begin{align*}\frac{125}{1000}\end{align*}
9. 110\begin{align*}\frac{1}{10}\end{align*}
10. 2100\begin{align*}\frac{2}{100}\end{align*}
11. 12\begin{align*}\frac{1}{2}\end{align*}
12. 14\begin{align*}\frac{1}{4}\end{align*}
13. 34\begin{align*}\frac{3}{4}\end{align*}
14. 36\begin{align*}\frac{3}{6}\end{align*}
15. 35\begin{align*}\frac{3}{5}\end{align*}

### Vocabulary Language: English

Decimal

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

Equivalent means equal in value or meaning.
fraction

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

Irrational Number

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

Place Value

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