Decimals and Fractions

Decimals and fractions represent the same thing -- parts of a whole.

While a "whole" can be cut into any number of fractional pieces (halves, thirds, fourths, eighths, tenths, etc), decimals are fractional pieces that have only powers of ten as their denominator: tenths, hundredths, thousandths, etc.

Since they represent the same fractional pieces, fractions can be converted into decimals and decimals can be converted into fractions.

Decimals to Fractions

Reading a decimal using its "place value name" leads directly to writing it as an equivalent fraction. For example, instead of saying "point two five" or "point twenty-five," saying "twenty-five hundredths" tells exactly what fraction is equivalent. Before simplifying, the denominator of the fraction will always be 10 or 100 or 1000 etc.

Fractions to Decimals

There are several ways to convert a fraction into its equivalent decimal.

1) If the fraction is already written with a denominator of 10 or 100 or 1000, simply saying the fraction's name tells you how to write the fraction as a decimal. You just have to know the names of the decimal places.

2) Sometimes you can easily convert a fraction into an equivalent fraction that has 10 or 100 or 1000 as its denominator.

3) If the denominator is not 10 or 100 or 1000 and it can't easily be converted into one that is 10 or 100 or 1000, you can convert any fraction into a decimal by looking at the fraction bar as a division sign.