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# Fractions as Decimals

## Dividing the denominator into the numerator

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Fractions as Decimals

### Let’s Think About It

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.

### 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.

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:

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

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

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.

To change  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.

The decimal value of  is .

### Guided Practice

Write the following fraction as a decimal.

One way is to use base ten values. First, find an equivalent fraction of  with a denominator of 100.

Then, convert the fraction to a decimal.  is also 25 hundredths.

The decimal value of  is 0.25.

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

The decimal value of  is 0.25.

### Examples

Convert each fraction to a decimal.

#### Example 1

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

The decimal value of  is .

#### Example 2

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

The decimal value of  is .

#### Example 3

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

The decimal value of  is .

License: CC BY-NC 3.0

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 . 6 out of 8 is also . Convert the fractions to decimals and compare their results.

First, convert  to a decimal. The denominator is a base ten number.

Then, convert  to a decimal. Divide 6 by 8.

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

Terry made more of his shots than Michelle.

### Explore More

Convert the following fractions as decimals.

1.
2.
3.

### Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 5.19.

### 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.

1. [1]^ License: CC BY-NC 3.0
2. [2]^ License: CC BY-NC 3.0

### Explore More

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