Question

1. The rational form of 0.254 and 54 has bar is in the form of, then (p + q) is ​

Answer 1

Answer: 14/55 is the right answer

Step-by-step explanation:

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Answer 2

SOLUTION

GIVEN

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

TO DETERMINE

The value of p + q

EVALUATION

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

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

So we have

p + q = 14 + 55 = 69

FINAL ANSWER

Hence the required value of p + q = 69

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