Fractions also may be written in *decimal* form (decimal fractions) as either terminating, coming to an end (for example 0.3 or 0.125), or having an *infinite* (never ending) *repeating* pattern (for example (0.666… or 0.1272727…).

#### Changing terminating decimals to fractions

To *change terminating decimals to fractions,* remember that all numbers to the right of the decimal point are fractions with denominators of only 10, 100, 1000, 10,000, and so forth. Next, use the technique of *read it, write it,* and *reduce it.*

##### Example 1

Change the following to fractions in lowest terms.

All rules for signed numbers also apply to operations with decimals.

#### Changing fractions to decimals

To *change a fraction to a decimal,* simply do what the operation says. In other words means 13 divided by 20. So do just that (insert decimal points and zeros accordingly).

##### Example 2

Change to decimals.

#### Changing infinite repeating decimals to fractions

Infinite repeating decimals usually are represented by putting a line over (sometimes under) the shortest block of repeating decimals. This line is called a *vinculum.* So you would write

to indicate .333 …

to indicate .515151 …

to indicate –2.1474747 …

Notice that only the digits under the vinculum are repeated.

Every infinite repeating decimal can be expressed as a fraction.

##### Example 3

Find the fraction represented by the repeating decimal .

Because 10 *n* and *n* have the same fractional part, their difference is an integer.

Therefore,

##### Example 4

Find the fraction represented by the repeating decimal .

Because 100 *n* and 1 *n* have the same fractional part, their difference is an integer.

Therefore,

##### Example 5

Find the fraction represented by the repeating decimal .

Because 100 *n* and 10 *n* have the same fractional part, their difference is an integer.

Therefore,