In this concept, you will learn how to write fractions and mixed numbers as terminating decimals.

### Writing Fractions and Mixed Numbers as Decimals

Fractions and decimals are both ways of describing numbers that are not whole numbers. Every fraction is equivalent to some decimal. To write a fraction as a decimal, remember that a fraction is really just a division expression. For example, is the same as .

Here are the steps for writing a fraction as a decimal.

- Rewrite your fraction as a division problem.
- Divide using long division. Add a decimal point and zeros to the dividend as needed.

Here is an example.

Convert

to a decimal.First, write

as a division problem.is the same as .

Next, use long division to divide. You will need to add a decimal point and zeros to the 3.

The answer is

.You can also convert mixed numbers to decimals. Here are the steps for writing mixed numbers as decimals.

- Convert the fractional part of the mixed number to a decimal using long division.
- Add the whole number part of the mixed number to the result from step 1.

Here is an example.

Convert

to a decimal.First, set aside the 3.

is the same as . Convert the to a decimal using long division.

Next, add the 3 from the original mixed number.

The answer is

.### Examples

#### Example 1

Earlier, you were given a problem about Erik and his Italian bread.

He needs

ounces of water to make his bread dough, but his scale only shows numbers in decimal form. Erik needs to figure out what number his scale should show when he has added the correct amount of water.Erik needs to convert

to a decimal.First, he should set aside the 10.

. He needs to convert the to a decimal using long division.

Next, he should add the 10 from the original mixed number.

The answer is Erik should look for his scale to show 10.625 when he has added the correct amount of water.

#### Example 2

Convert to a decimal.

First, set aside the 4.

is the same as . Convert the to a decimal using long division.

Next, add the 4 from the original mixed number.

The answer is

.#### Example 3

Convert

to a decimal.First, write

as a division problem.is the same as .

Next, use long division to divide. You will need to add a decimal point and a zero to the 1.

The answer is

.#### Example 4

Convert to a decimal.

First, write

as a division problem.is the same as .

Next, use long division to divide. You will need to add a decimal point and a zero to the 3.

The answer is

.#### Example 5

Convert

to a decimal.First, set aside the 4.

. Convert the to a decimal using long division.

Next, add the 4 from the original mixed number.

The answer is

.

### Review

Convert each fraction or mixed number to a decimal.

### Review (Answers)

To see the Review answers, open this PDF file and look for section 3.15.

### Resources