# Conversions between Decimals and Fractions

## Objectives

After completing this unit you should be able to:

• Convert a fraction to a decimal.
• Convert a decimal to a fraction.

As you probably know, fractions can always be written as decimals. For example, 1/2 can be written as 0.5. In this section we will give a quick review of converting from fractions to decimals and then from decimals to fractions. Converting from fractions to decimals is fairly easy. Any number written in the form a/b can be converted to a decimal by dividing a by b. For example, if you do the division of 3/4 then you will get .75.

Let's try a quick example of converting a fraction to a decimal.

### Example

Express the fraction 5/8 in decimal form.
The fraction 5/8 can be expressed as .625.

To convert a fraction 5/8 to a decimal we need to perform the division:

 The fraction 5/8 can be written in the form of: the division of Now perform the division of .

Converting from a decimal to a fraction is more complicated. It requires paying attention to the decimal places. For example, .5 is 5 tenths. This means we have 5 over ten, the fraction 5/10. This fraction can then be reduced to its simplest form of 1/2. If our decimal is 0.05 we read it as 5 hundredths, which would change it to 5 over 100, or 5/100 which simplifies to 1/20. So, to convert a decimal to a fraction you should use the following steps:

1. Read the numerical decimal, paying close attention to the ending.
2. Place the number in the decimal, written as a whole number, in the numerator of the fraction.
3. Look at the ending of the decimal as read in step 1. Take the 'ths' off the end and place the numeric value of the number you have in the denominator.
4. Simplify the fraction.

Let's try an example of working through these steps.

### Example

Express the decimal .045 as a fraction.
The answer is 9/200

1. Read the numerical decimal, paying close attention to the ending.
The decimal .045 is forty-five thousandths
2. Place the number in the decimal, written as a whole number, in the numerator of the fraction.
3. Look at the ending of the decimal as read in step 1. Take the 'ths' off the end and place the numeric value of the number you have in the denominator.
 The ending of our decimal is thousandths. This means we need to place a 1000 (thousand) in the denominator.
4. Simplify the fraction.
The fraction 45/1000 can be simplified to 9/200. (NOTE: If you need some review on reducing fractions to their simplest form, you should review Book I in this series.)

Now let's try a practice for converting between decimals and fractions.