Terminating Decimal

Suppose we have a fraction, 3/8

${\dfrac{3}{8}}$ = 0.375

The division ends as it has no remainder. So the number 0.375 is a terminating decimal.

Thus terminating decimals are numbers that have a finite number of digits after the decimal point. In other words, a decimal number that has an end is referred to as a terminating decimal.

Some examples of terminating decimals are shown in the following diagram having three and four decimal places.

So, is 3/5 terminating decimal?

${\dfrac{3}{5}}$ = 0.6

The division ends at 0.6. 3/5 is a terminating decimal.

In contrast, the decimal numbers having infinite number of digits after the decimal point are non-terminating decimals. For example, 0.777777… is a non-terminating decimal.

Identifying Terminating Decimals

Steps to identify terminating decimals are:

1. The number has to be a rational number.
2. There is a finite number of digits after the decimal point.

Now, let us learn the opposite concept, i.e., non-terminating decimals.

Solved Examples

Convert 9/11 to decimal. Identify the decimal as terminating or non-terminating.

Solution:

9  ÷ 11 = 0.81818181…..
It is a non-terminating and repeating decimal as the division never ends, and the digits get repeated infinitely.

convert 5/8 to decimal. Identify the decimal as terminating or non-terminating.

Solution:

5/8 = 0.625. The division ends at 5. The decimal is terminating.