Decimals and their Equivalent Fractions

Question: What is the equivalent fraction for the decimal 4.422?

Further Explanation

The method above shows how to obtain an equivalent fraction from a decimal. It is even easier to find the decimal equivalent of a fraction. All you have to do is to use division.

So, for example, the decimal equivalent of the fraction is 0.25 as 1.00 divided by 4 will give this result. Similarly the fraction can be expressed as a decimal by dividing 3 by 5 to obtain 0.6

A similar way of achieving this is to find an equivalent fraction that has either 10 or 100 or 1000 etc. as the denominator. In this way we can determine the fraction equivalent from the resulting numerator. For example,

and so the decimal equivalent is 0.6.

Similarly for more complicated fractions such as . We can find its decimal equivalent by multiplying both numerator and denominator by 25. This gives

and so the decimal equivalent is 0.075

If you are still feeling confused about equivalent decimals and fractions, then think of a number line in which all numbers are represented. A small part of such a number line is shown below with numbers shown as decimals above the line and fractions below the line

You can readily see, for example, that

Note: What happens when the fraction cannot be expressed as an equivalent fraction with a numerator of 10 or 100 or 1000 etc.?

An example of this is the fraction . You can though divide 1.0000000......... by 3 to give 0.33333.......... This is called a recurring decimal, and is often denoted by putting a dot on top of the number (or numbers) that repeat. So we can write

There are many other fractions that give rise to recurring decimals, often with a group of digits that repeat. For example