Question

the rational form of 0.254 bar is in the form of p/q, then(p+q) is

Answer 1

it is given in the question

0.254 bar in the form of p/q, then what is (p+q)

$\begin{array}{l}\mathrm{x}=0 . \overline{245} \\\mathrm{x}=0.245245245 \ldots . . \\1000 \mathrm{x}=245.245245 \ldots . \\(1000 \mathrm{x}-\mathrm{x})=(245.245245 \ldots)-(0.245245 \ldots) \\999 \mathrm{x}=245 \\\mathrm{x}=\frac{245}{999}\end{array}$

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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