Terminating Decimal Definition
Those decimals that have a finite, limited, or known number of digits after the decimal point are called Terminating Decimals. For Example, 3.14, 2.578, and 1.987 are terminating decimals because all of these have limited numbers after the Decimal Point.
Such decimals are used to represent a whole number and a fraction collectively in a single term. In a terminating decimal, the left side of the decimal point gives the whole number while the right side shows the fractional part. For example, in 3.14, “3” represents the whole number while “14” shows the decimal fraction.
Note:
Read about Whole Numbers and a Fraction here.
Table of Contents
What is the opposite of Terminating a Decimal?
In Mathematics, Decimals are divided into two major types. One of which is terminating decimals about which we are reading here. In contrast, the other type is called Non-terminating decimals. These decimals have infinite or unknown numbers after the decimal point.
Such numbers are normally represented by putting “Three Dots” after the last number on the right side of the decimal point. For example, 3.3333333… is a non-terminating decimal because we don’t know the ending point of this decimal.
Note:
Read about Non-terminating Decimals here.
How to convert a fraction into a termination decimal?
The only way to convert a fraction into a terminating decimal is by division. We only have to divide the numerator by the denominator of the fraction to get this decimal. While dividing, we can get the following three types of numbers.
- Whole number
- Terminating Decimal
- Non-terminating Decimal
It means that we can get the answer of a fraction in any of these formats. So, there is no restriction that we will always get a terminating decimal by dividing a fraction.
Note:
Read about Division, Numerator, and Denominator here.
How to identify a terminating decimal?
As mentioned above, a terminating decimal has a limited number of digits after the decimal point. But we can also identify these numbers even without solving the fraction. To do so, we only have to check the denominator of the given fraction.
If the denominator can be written in the power of 2 and 5, it means that the fraction will give a terminating decimal as the answer. It is the simplest and easiest way to identify a decimal of this type without division.
Fun facts about terminating decimals
- All terminating decimals are also rational numbers.
- The left side of the terminating decimal gives the whole part of the fraction.
- All fractions with a denominator that can be written in the form of an exponent of 2 and 5 are terminating decimals.
- A non-terminating decimal can be converted to a terminating decimal with the Round-Off technique.
FAQ's
What does terminating mean?
Terminating means to end. In Mathematics, it is used for those decimals that are going to an end after some points.
How to check the termination of a fraction without division?
You can check it just by looking at the denominator of the fraction. If the denominator can be written as an exponent of 2 and 5, the fraction will give a terminating decimal.
Is Pi a terminating decimal?
No, Pi is not a terminating decimal because the numbers after the decimal point are now known.
Are terminating and repeating decimals the same?
No, terminating decimals are those that have limited numbers after the decimal point. On the other hand, repeating decimals is a type of non-terminating decimal that has a specific pattern repeating itself after the decimal point.
