# Terminating decimals

In this chapter we will learn the concept of terminating decimals, its definition and solved examples.

## Terminating decimals definition

The decimals which have fixed number after the decimal points are called terminating decimals.

It is the decimal whose digits end after a certain point.

### Examples of Terminating decimals

7.13
It’s a terminating decimal as the decimal ends after two decimal point.

100.73684
The number is a terminating decimal as the decimal ends after 5 decimal places.

63.135
It’s a terminating decimal as the number ends after 3 decimal place.

Conclusion
Terminating decimal is the number whose value ends after certain decimal point.

## Fraction with terminating decimal value

We know that when we divide the numerator and denominator value of fraction we get decimal numbers.

Now after division of fraction we may get terminating or non terminating decimal values depending on type of fractions.

Given below are examples of fractions with decimal values.

Example 01
Find decimal value of fraction 100/8

Solution
Dividing numerator with denominator.

On dividing the fraction we get ⟹ 12.5
The number is a terminating decimal as the number ends after one decimal point.

Example 02
Express 100/3 in decimal form

Solution
Dividing numerator by denominator we get;

On dividing the fraction we get ⟹ 33.3333 . . . .

The number is a non terminating decimal because the number after decimal points are unending.

Example 03
Find the value of fraction 17/5

Solution
Dividing numerator by denominator we get;

On dividing the fraction we get ⟹ 3.4

The number 3.4 is a terminating decimal since its value ends after one decimal point.

Example 04
Express the fraction 25/4 in decimal form

Solution
Dividing numerator by denominator.

On dividing the fraction we get ⟹ 6.25

The number 6.25 is a terminating fraction since the number get terminated after 2 decimal place.

Example 05
Express the fraction 39/6 in decimal form.

Solution
Dividing the numerator and denominator.

After dividing the fraction we get ⟹ 6.5

The number is terminating decimal since the number gets completed after one decimal point.

## Terminating decimals – Solved problems

(01) Identify if the below decimals are terminating or non terminating.

(a) 6.65
(b) 6.77777. . .
(c) 9.85902
(d) 16.63
(e) 3.33333 . . .

Solution

(a) 6.65
Its a terminating decimal since it contain finite digits after decimal points.

(b) 6.77777. . .
It’s a non terminating decimal since it contains unending number of digits after decimal point.

(c) 9.85902
Its a terminating decimal.
It contain 5 numbers after decimal point.

(d) 16.63
It’s a terminating decimal which contains 2 numbers are decimal point.

(e) 3.33333 . . .
It’s a non terminating decimal since it contain unending numbers after decimal points.

(02) Find the decimal value of fraction and identify if it’s terminating or non terminating decimals

(i) 13/5
(ii) 199/2
(iii) 100/6
(iv) 11/20

Solution

(i) 13/5

Dividing numerator by denominator

After dividing the fraction we get ⟹ 2.6

The number is a terminating fraction since it contain finite number after decimal point.

(ii) 199/2

Dividing the numerator and denominator.

After division we get ⟹ 99.5
The number is a terminating decimal since it contain finite digits after decimal point.

(iii) 100/6

Dividing numerator by denominator.

After division we get ⟹ 16.666666 . . . .

This is a non terminating decimal since it contains infinite numbers after decimal point.

(iv) 11/20

Dividing numerator and denominator.

After division we get ⟹ 0.55

This is a terminating decimal since it contain 2 numbers after decimal points.