Question

CHOOSE THE CORRECT ANSWERS
1. The rational form of 0.254 bar is in the form of p/q then ip + q) is
a 14
b. 55
c. 69
d. 79​

Answer 1

The rational form of $\sf 0.2 \overline{54}$ is in the form of p/q then p + q is 69

Given : The rational form of $\sf 0.2 \overline{54}$ is in the form of p/q

To find : The value of p + q is

a. 14

b. 55

c. 69

d. 79

Solution :

Step 1 of 3 :

Write down the given number

The given number is $\sf 0.2 \overline{54}$

Step 2 of 3 :

Express it in the form p/q

$\sf Let \: \: x = 0.2 \overline{54}$

Then

x = 0.2545454 . . . . - - - - - - - (1)

Multiplying both sides by 10 we get

10x = 2.545454 . . . . - - - - - - - (2)

Again Multiplying both sides by 100 we get

1000x = 254.545454 . . . . - - - - - - - (3)

Equation 3 - Equation 2 gives

990x = 252

$\displaystyle \sf{ \implies x = \frac{252}{990} }$

$\displaystyle \sf{ \implies x = \frac{14}{55} }$

Which is of the form p/q

Then p = 14 , q = 55

Step 3 of 3

Find the value of p + q

We have

p + q = 14 + 55 = 69

Hence correct option is c. 69

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