Decimals are a way of expressing fractions in an equivalent form that's often easier to work with.

For example, let's consider the fraction "one-tenth":

To express this fraction as a decimal, we write a zero followed by a dot (called the decimal point) followed by the fraction's numerator:

Any fraction with a denominator of can similarly be written as a decimal.

For example, we can express six-tenths as a decimal as follows:

Note: Fractions with a denominator of are examples of decimal fractions. We'll meet more decimal fractions in this lesson.

Fractions with a denominator of can also be written as decimals. For this reason, they are also called decimal fractions.

When writing a fraction with a denominator of we must remember the following crucial fact:

Every fraction with a denominator of will have precisely two digits after the decimal point.

Let's see some examples:

• We express the fraction seventy-eight hundredths as a decimal as follows: Notice that this decimal has two digits after the decimal point.

• We express the fraction three-hundredths as a decimal as follows: Notice that this decimal also has two digits after the decimal point.

Watch Out! When the numerator is smaller than we must write an extra zero after the decimal point and before the numerator's digit. The following answers are not equivalent to

Finally, the fraction is known as one-hundredth, and can also be written as a decimal:

Any fraction with a denominator of can be written as a decimal with decimal places, in the same way as before. Fractions with a denominator of are another example of decimal fractions.

Some examples of decimal fractions with denominator are shown below:

The fraction is known as one-thousandth, and can also be written as a decimal: