Decimals and Fractions

**Decimals and Fractions**

**C**

**hange a Decimal to a Fraction**

To convert a decimal to a fraction, remove the decimal point from the number and place the decimal part over a denominator. That denominator should be equal to the place value of the last digit in the decimal.

Reduce the fraction to simplest form.

Example: Write 0.36 as a fraction in simplest form.

**6** is in the hundredths' place, so the denominator is 100.

**Change a Fraction to a Decimal**

To change a fraction to a decimal, divide the numerator of the fraction by the denominator.

Some decimals have repeating digits. Repeating decimals can be written with a bar over the digit(s) that repeat.

0.33333 = 0. **One digit repeats**

0.616161 = 0. **Two digits repeat**

Example: Change the following expression to a decimal

First divide until the quotient ends or repeats

7 22 = 0.3181818

Write a bar over the parts of the quotient which repeat

0.3181818 0.3

Therefore

**Compare Fractions and Decimals**

Decimals, like whole numbers and fractions, can be graphed as points on a line. In order to compare the values of fractions and decimals, a number line may be used. Numbers to the left on a number line are less than numbers to the right.

Example

Compare 0.65 to the following fraction

It is often helpful to convert one number to another form to compare it to a given number. For example, when comparing a fraction to a decimal, you could choose to write both in decimal form.

ones | tenths | hundredths | ||

0.65 | 0 | . | 6 | 5 |

0 | . | 2 | 3 |