Terminating decimals are the numbers that have a fixed or a finite number of digits after the decimal point. 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. In this article, we will learn what are terminating decimals and the ways to recognize these numbers.
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|1.||Definition of Terminating Decimal|
|2.||How to Recognize Terminating Decimal?|
|3.||Examples of Terminating Decimal|
|4.||FAQs on 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 expansionNon-terminating recurring decimal expansionNon-terminating non-recurring 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 non-terminating recurring decimal expansion. For example, 23.5 is a terminating decimal number because it has 1 digit after the decimal point.
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 a simplified rational number in the form 2p5q or 2p or 5q, where p,q∈N, then the number has a terminating decimal expansion.A terminating decimal number always has a finite number of digits after the decimal point.
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 difficult to express a non-terminating decimal (non-repeating) in p/q form, where q is not equal to 0.
The table given below shows examples which will help you in identifying terminating decimals better.
|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/(23). Clearly, the denominator is of the form 2p. So, it is a terminating decimal number.|
|√2||This is not a rational number. So, it is a non-terminating 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 always a rational number.If the denominator of a rational number cannot be expressed in form 2p5q or 2p or 5q, where p,q∈N, then the rational number has a non-terminating recurring decimal expansion.
Topics Related to Terminating Decimal
Check these articles related to the concept of terminating decimal numbers.
Example 1: The length and breadth of a rectangle are 7.1 inches and 2.5 inches respectively. Determine whether the area of the rectangle is a terminating decimal or not.Solution: Given, the length of rectangle is 7.1 inches and the breadth of rectangle = 2.5 inches.Area of Rectangle = Length × Breadth = 7.1 inches × 2.5 inches =17.75 inches2As 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 non-terminating 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, 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 to find which among them is a terminating decimal?Solution: The fractions can be expressed as:2/7 = 0.285714….8/20 = 0.410/30 = 0.333…5/32 = 0.15625
Therefore, the fractions which are terminating decimals are 8/20 and 5/32.
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