Rational Numbers can be expressed in the form of Fractions. We can convert the rational numbers to decimal form by simply dividing the numerator with the denominator. In this article, we will help you determine if a rational number is terminating or non-terminating and the formula for telling so. Go through the further sections and find various models of problems on rational numbers as decimal numbers. Get a clear idea of the concept and easily understand the questions present.
How to check if a Rational Number is Terminating or Non-Terminating?
To Identify if a rational number is terminating or not you can use the following formula \(\frac { x }{ 2^m * 5^n } \) where x ∈ Z is the numerator of the given rational fractions and the denominator y can be written in the powers of 2 and 5 where m ∈ W; n ∈ W.
If you can write the rational number in the above form then it is called a terminating decimal. If it can’t be written in the above form it is called a non-terminating decimal.
Do Refer:
- Decimal Representation of Rational Numbers
- Rational Numbers in Terminating and Non-Terminating Decimals
- Recurring Decimals as Rational Numbers
Solved Examples on Expressing Rational Numbers as Decimal Numbers
Example 1.
Check whether \(\frac { 3 }{ 4 } \) is a terminating or non-terminating decimal. Also, convert it to a decimal number?
Solution:
Given Rational Number is \(\frac { 3 }{ 4 } \)
Let us check if it is terminating or not initially, To do so we need to convert the given rational number to the form of \(\frac { x }{ 2^m * 5^n } \)
= \(\frac { 3 }{ 2^2 * 5^0 } \)
Since we can express it in the form of \(\frac { x }{ 2^m * 5^n } \) it is a terminating decimal.
\(\frac { 3 }{ 4 } \) converted to decimal form is 0.75
Example 2.
Check whether \(\frac { 7 }{ 3 } \) is a terminating or non-terminating decimal. Also, change it to decimal number?
Solution:
Given Rational Number is \(\frac { 7 }{ 3 } \)
Let us check if it is terminating or not initially, To do so we need to convert the given rational number to the form of \(\frac { x }{ 2^m * 5^n } \)
Since we can’t express it in the form of \(\frac { x }{ 2^m * 5^n } \) it is a non-terminating decimal.
\(\frac { 7 }{ 3} \) converted to decimal form is 2.333……
Example 3.
Check whether \(\frac { 5 }{ 24 } \) is terminating or non-terminating decimal and express it in decimal form?
Solution:
Given Rational Number is \(\frac { 5 }{ 24 } \)
Let us check if it is terminating or not initially, To do so we need to convert the given rational number to the form of \(\frac { x }{ 2^m * 5^n } \)
= \(\frac { 5 }{ 2^2 * 6^1 } \)
Since we can express it in the form of \(\frac { x }{ 2^m * 5^n } \) it is a terminating decimal.
\(\frac { 5 }{ 24 } \) converted to decimal form is 0.2083