Question

Is 22/7 a rational number?

Answer 1

Yes 22/7 Is a rational number because it can be represented in the form of p/q where q is not equal to 0

What is a rational number?

• A rational number is a number which can be represented in the form of p/q where q is not equal to 0.
• A rational number has a terminating decimal expansion or recurring (non-terminating) decimal expansion.

For example:-

• 0.375

= 375/10³

= (3×5³)/(2³×5³) [5³/5³= 1]

= 3/2³

Here we have converted a real number whose decimal expansion terminates into a rational number of the form p/q, where p and q are coprime.

How to convert a terminating decimal expansion into p/q form?

(i) 0.323232.....

Let x = 0.323232.... --------> (i)

100x = 32.3232..... --------> (ii)

Subtracting eq (i) from eq (ii)

100x = 32.3232.....

- x = 0.3232.....

= 99x = 32

=> x = 32/99 [p/q form]

Hence we converted a terminating decimal expansion into rational number of the form p/q where q is not equal to 0.