Arithmetic : Decimals

Decimal Fractions

The decimal system can include fractions by using a period called the decimal point.
A decimal fraction comprises the decimal point followed by a collection of digits. Its value is less than 1.
For example, 0.7, .49, .823 and 0.0561 are decimal fractions.
Note that the zero to the left of the decimal point is optional.

Every decimal fraction can be represented by a fraction, whose numerator is given by the digits to the right of the decimal point and whose denominator is given by 1 followed by zeros equal in number to the digits to the right of the decimal point.

For example, 0.823 can be represented as 823/1000, where the numerator is 823 and the denominator is 1 followed by 3 zeros (since there are 3 digits to the right of the decimal point).