Question

Express 0.717171.... decimals in the form p/q, where p and q are integers
and q ≠ 0.

Answer 1

Step-by-step explanation:

Given:-

0.717171...

To find:-

Express 0.717171.... decimals in the form

p/q, where p and q are integers and

q ≠ 0.

Solution:-

Given number = 0.717171....

Let X = 0.717171....--------------(1)

Since ,the periodicity is 2 then multiply (1) with 100

=> 100×X = 0.717171...×100

=> 100X = 71.717171... --------(2)

On Subtracting (1) from (2) then

100X = 71.717171...

X = 0.717171...

(-)

________________

99X = 71.000000...

_________________

=> 99X = 71

=> X = 71/99

0.717171... = 71/99

Answer:-

The p/q form of the given number 0.717171... is 71/99

Used formula:-

Periodicity:-

The number of digits in the recurring part of the decimal number is called its periodicity.