Converting Decimals to Fractions

Decimal numbers can be written in decimal form or as fractions. How do we convert from one to the other?

I. Converting decimals to fractions

Convert a decimal number written in decimal form into a fraction.

Example 1: The number 41.3 may be read as 41 units and 3 tenths and written $41+\frac{3}{10}$ .

We can also say that 41.3 equals 413 tenths, i.e.: $41.3+\frac{413}{10}$ .

Example 2: Similarly, we can write: $56.29=56+\frac{2}{10}+\frac{9}{100}=56+\frac{29}{100}=\frac{5600}{100}+\frac{29}{100}=\frac{5629}{100}$ .

This means that 56.29 can be read as 56 units, 2 tenths, and 9 hundredths; or as 56 units and 29 hundredths; or as 5,629 hundredths.

II. Converting fractions to decimals

Convert a decimal number written as a fraction into decimal form.

The fractions used have denominators of 10, 100, or 1,000. These are decimal fractions. We simply have to divide by 10, 100, or 1,000, as indicated by the fractions, and then add them to the numbers obtained.

Examples:

$35+\frac{89}{100}=35+0.89=35.89$

$906+\frac{7}{1000}=906+0.007=906.007$

In addition to the division process, we could just read the number and place the digits in their correct place value. In the first of the two examples above, we would read the fraction as 35 and 89 hundredths, which converts to the decimal 35.89.

Read more:
Reading and Writing Decimal Numbers
Multiplying or Dividing a Decimal Number by 10, 100, or 1,000
Multiplying Decimal Numbers
Dividing Decimal Numbers
The Effect of Addition and Multiplication on the Order of Numbers
Describing Different Types of Numbers
Dividing Whole Numbers with a Remainder
Comparing and Ordering Decimal Numbers
Adding and Subtracting Decimal Numbers