# Terminating decimal definition explained

Learn and know the definition of terminating decimal in math. The word “terminating” we will observe mostly in the rational numbers concept. Learning what is terminating decimal will help in finding the number whether it is a rational or not a rational.

We know that any given rational number will be of the form of a terminating decimal or non terminating repeating decimal. Non terminating repeating decimal is also called as non terminating recurring decimal. First we will know the meaning of the word “terminating” then we will define terminating decimal. Terminating means ending. Now we will know what is terminating decimal definition.

## Definition of terminating decimal as follows:

If you are doing division of any numbers, and if in the division process after some steps if the remainder is zero (i.e. if the division process is ending) then the quotient is called as terminating decimal. From the definition of terminating decimal, we can also say that if in a decimal number there exists finite number of decimal places then it is also called terminating decimal.

Examples:

Let us take one division problem, am taking $\frac { 17 }{ 5 }$, after dividing 17 by 5, we get the quotient as 3.4 and remainder zero. So the quotient 3.4 is called as a terminating decimal.

Consider one more division problem, $\frac { 476 }{ 25 }$, if we divide 476 by 25, we get quotient 19.04 and remainder zero. So here the quotient 19.04 is called terminating decimal.

Divide 40 by 3, and find quotient and remainder. If we divide 40 by 3, we get quotient as 13.33333…..and remainder is not zero. As remainder is not zero so the quotient 13.3333….. Not a terminating decimal.

Some more examples of terminating decimals are 223.214, 98.214578, 44712.3625, 77.006985, 11.5544, 3.654, and 9.32014 and so on. All these terminating decimals represent rational numbers.

Hope, now you know what is the meaning of terminating decimal.