Terminating Decimals
Decimal numbers are used to represent the partial amount of whole, just like fractions. In this lesson, we will focus on the type of decimal numbers, that is, terminating decimal numbers. The word terminate means to bring to an end'. In terms of decimal, it is a number that ends. Terminating decimals are the numbers that have the digits ending after the decimal point. In this short lesson, we will learn what are terminating decimals and the ways to recognize these numbers. You can also try your hand at solving a few interesting practice questions at the end of the page.
Definition of Terminating Decimal
The number which has a finite number of digits after the decimal point is referred to as a terminating decimal. You have already learned about decimal numbers. Decimal expansions are of three types:
 Terminating decimal expansion
 Nonterminating recurring decimal expansion
 Nonterminating nonrecurring decimal expansion
Here we will discuss about terminating decimal expansion. A number has a terminating decimal expansion if the digits after the decimal point terminate. The fraction 5/10 has the decimal expansion 0.5, which is a terminating decimal expansion because digits after the decimal point end after one digit. A rational number has either a terminating decimal expansion or a nonterminating recurring decimal expansion. For example, 23.5 is a terminating decimal number because it has 1 digit after the decimal point.
How To Recognize a Terminating Decimal?
Here are a few points that will help you to recognize a terminating decimal number.
 A number that is not rational is never a terminating decimal number.
 If you can express the denominator of simplified rational number in the form 2^{p}5^{q}, where \(p,q \in \mathbb{N}\),then the number has terminating decimal expansion.
 A terminating decimal number always has a finite number of digits after the decimal point.
Examples of Terminating Decimal
In order to differentiate whether a given decimal is terminating or non terminating decimal, it is necessary to understand their basic differences like:
 Terminating decimal has finite digits and non terminating decimals do not have finite digits.
 It is easy to represent a terminating decimal in the form of p/q but it is not possible to express a non terminating decimal in p/q form, where q is not equal to 0.
The below table shows examples which will help you in identifying terminating decimals better.
Number  Terminating or Nonterminating Decimal 

2.675  Since there are 3 digits after the decimal point, it is a terminating decimal number 
3/8  We can write 3/8 as 3/8= 3/(2^{3})= (3 × 5)/(2^{3}× 5). Clearly, the denominator is of the form 2^{p}5^{q}. So, it is a terminating decimal number. 
√2  This is not a rational number. So, it is a nonterminating decimal number. 
Tips to Remember
 Terminating decimal number has a finite number of digits after the decimal point.
 A number with a terminating decimal is a rational number.
 If the denominator of a rational number can be expressed in the form 2^{p}5^{q}, where \(p,q \in \mathbb{N}\), then the decimal expansion of the rational number terminates.
 If the denominator of a rational number cannot be expressed in the form 2^{p}5^{q}, where \(p,q \in \mathbb{N}\), then the rational number has a nonterminating recurring decimal expansion.
Topics Related to Terminating Decimal
Solved Examples

Example 1: The length and breadth of a rectangle is 7.1 inches and 2.5 inches.Determine whether the of the area of the rectangle is a terminating decimal or not.
Solution: Given, the length of rectangle is 7.1 inches and breadth of rectangle = 2.5 inches.
Area of Rectangle = Length × Breadth =7.1 inches × 2.5 inches =17.75 inches^{2}
As the number of digits is finite after the decimal point, the area of rectangle is a terminating decimal expansion. 
Example 2: Look at the following pie charts. Which one of the pie charts represent a terminating decimal number?
Solution: From the above figures we understand:
a)The shaded portion of the first pie chart represents the number 4/6. 4/6 can be simplified as 2/3. The decimal expansion of 2/3 is 0.66... which is nonterminating and repeating decimal expansion.
b)The shaded portion of the second pie chart represents the number 2/8. 2/8 can be simplified as 1/4. The decimal expansion of 1/4 is 0.25 which is terminating decimal expansion.
\(\therefore\) the b) pie chart represents the terminating decimal expansion. 
Example 3: Mary's teacher wrote 4 fractions on board, 2/7, 8/20, 10/30 and 5/32. Help Mary find which among them is a terminating decimal.
Solution: The fractions can be expressed as:
2/7 = 0.285714....
8/20 = 0.4
10/30 = 0.333...
5/32 = 0.15625\(\therefore\) The fractions which are terminating decimals are 8/20 and 5/32.
FAQs on Terminating Decimal
What is an Example of Terminating Decimal?
A decimal number which has finite number of digits after the decimal point. The example of terminating decimal is 0.5.
Is 7/8 a terminating decimal?
The decimal representation 7/8 is 0.875. So, it is a terminating decimal.
Is 11/20 a terminating decimal?
The decimal representation 11/20 is 0.55. So, it is a terminating decimal.
Is 3.3 a terminating decimal?
Yes, 3.3 is a terminating decimal because the digits after the decimal point come to an end. The number of digits after the decimal point is finite which is counted as 1.
Is Pi a terminating decimal?
No, pi is not a terminating decimal as the value of pi is, 3.141592653589793238... It does not terminate and is not repetitive either which makes it an irrational number.
Is 0.75 a terminating decimal?
Yes, 0.75 is a terminating decimal because the digits after the decimal point come to an end. The number of digits after the decimal point is counted as 2.