Terminating decimals are the numbers that have a addressed or a finite number of digits after the decimal allude. Decimal numbers are provided to represent the partial amount of entirety, simply favor fractions. In this leschild, we will emphasis on the form of decimal numbers, that is, terminating decimal numbers. The word 'terminate' indicates to bring to an end. In regards to decimal, it is a number that ends. In this article, we will certainly learn what are terminating decimals and also the ways to recognize these numbers.

You are watching: What is the definition of terminating decimal

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 variety of digits after the decimal point is referred to as a terminating decimal. You have actually currently learned about decimal numbers. Decimal expansions are of 3 types:

Terminating decimal expansionNon-terminating recurring decimal expansionNon-terminating non-recurring decimal expansion

Here we will talk about around terminating decimal growth. A number has actually a terminating decimal growth if the digits after the decimal allude terminate. The fraction 5/10 has the decimal expansion 0.5, which is a terminating decimal growth bereason digits after the decimal allude end after one digit. A rational number has either a terminating decimal expansion or a non-terminating recurring decimal growth. For example, 23.5 is a terminating decimal number bereason it has actually 1 digit after the decimal point.

*


Here are a couple of points that will certainly assist you to identify a terminating decimal number.

A number that is not rational is never before a terminating decimal number.If you can expush the denominator of a streamlined rational number in the develop 2p5q or 2p or 5q, wbelow p,q∈N, then the number has a terminating decimal expansion.A terminating decimal number constantly has a finite number of digits after the decimal allude.

In order to differentiate whether a offered decimal is terminating or non terminating decimal, it is important to understand also their fundamental distinctions like:

Terminating decimal has actually finite digits and non terminating decimals execute not have actually finite digits.It is straightforward to represent a terminating decimal in the develop of p/q however it is tough to express a non-terminating decimal (non-repeating) in p/q develop, wbelow q is not equal to 0.

The table provided below mirrors examples which will certainly aid you in identifying terminating decimals much better.

NumberTerminating or Non-terminating Decimal
2.675Because tbelow are 3 digits after the decimal allude, it is a terminating decimal number.
3/8We can compose 3/8 as 3/8= 3/(23). Clbeforehand, the denominator is of the form 2p. So, it is a terminating decimal number.
√2This is not a rational number. So, it is a non-terminating decimal number.

Tips to Remember

Terminating decimal number has actually a finite variety of digits after the decimal point.A number with a terminating decimal is constantly a rational number.If the denominator of a rational number cannot be expressed in create 2p5q or 2p or 5q, wright here p,q∈N, then the rational number has a non-terminating recurring decimal expansion.

Topics Related to Terminating Decimal

Check these articles pertained to the concept of terminating decimal numbers.


Example 1: The size and also breadth of a rectangle are 7.1 inches and 2.5 inches respectively. Determine whether the location 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 variety of digits is finite after the decimal point, the area of rectangle is a terminating decimal expansion.

Example 2: Look at the complying with pie charts. Which one of the pie charts reexisting a terminating decimal number?

*

Solution: From the over figures we understand:a)The shaded percent of the first pie chart represents the number 4/6. 4/6 deserve to be streamlined as 2/3. The decimal development of 2/3 is 0.66... which is non-terminating and repeating decimal development.b)The shaded percent of the second pie chart represents the number 2/8. 2/8 can be streamlined as 1/4. The decimal expansion of 1/4 is 0.25 which is terminating decimal growth.Because of this, b) pie chart represents the terminating decimal growth.


Example 3: Mary's teacher created 4 fractions on board: 2/7, 8/20, 10/30 and also 5/32. Help Mary to uncover 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

As such, the fractions which are terminating decimals are 8/20 and 5/32.

See more: What Is A Group Of Larks Called ? What Is A Group Of Larks Called


Sjust how Equipment >

go to slidego to slidego to slide



Have concerns on standard mathematical concepts?
Become a problem-solving champ using logic, not rules. Learn the why behind math through ourlutz-heilmann.info’s certified specialists.