Question

The rational form of 0.254 is in the form of
then (p+q) is
a) 14
b) 55
c) 69
d) 79​

Answer 1

the rational form of 0.254 is the form of then (p+q)is 69

Answer 2

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

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

To find : To choose the correct option

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 the number 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

Step 3 of 3 :

Find the value of p + q

From above we get p = 14 , q = 55

So we have

p + q = 14 + 55 = 69

Hence the correct option is c) 69

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