Solved Examples

Example 1:

Identify each of the following as irrational or rational: ¾ , 90/12007, 12 and √5.

Solution:

Since a rational number is the one that can be expressed as a ratio. This indicates that it can be expressed as a fraction wherein both denominator and numerator are whole numbers.

• ¾ is a rational number as it can be expressed as a fraction. 3/4 = 0.75
• Fraction 90/12007 is rational.
• 12, also be written as 12/1. Again a rational number.
• Value of  √5 = 2.2360679775…….. It is a non-terminating value and hence cannot be written as a fraction. It is an irrational number.

Example 2:  

Identify whether a mixed fraction, 1¹/₂ is a rational number.

Solution: 

The Simplest form of 1¹/₂ is 3/2

Numerator = 3, which is an integer

Denominator = 2, is an integer and not equal to zero.

So, yes, 3/2 is a rational number.

Example 3:

Determine whether the given numbers are rational or irrational.

(a) 1.75 (b) 0.01   (c) 0.5  (d) 0.09   (d) √3

Solution:

The given numbers are in decimal format. To find whether the given number is decimal or not, we have to convert it into the fraction form (i.e., p/q)

If the denominator of the fraction is not equal to zero, then the number is rational, or else, it is irrational.

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