Question

Express 1.0251515151.......... in p/q form where p and q are integers and q is not equal to 0.​

Answer 1

Question :- Express 1.0251515151.......... in p/q form where p and q are integers and q is not equal to 0. ?

Solution :-

Let us assume that, given expression is equal to x.

→ x = 1.0251515151____________ ---------- Eqn.(1)

Multiply both sides by 100 we get,

→ 100x = 102.51515151_________ ---------- Eqn.(2)

Again Multiply by 100 both sides we get,

→ 10000x = 10251.515151_______ -------- Eqn.(3)

Subtracting Eqn.(2) from Eqn.(3) we get,

→ 10000x - 100x = (10251.515151__) - (102.515151__)

→ 9900x = 10149

→ x = (10149/9900) (Ans.)

Hence, p/q form of given expression is (10149/9900).

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Answer 2

$Let \: x = 1.025\bar{15} \: --(1)$

/* Multiplying equation (1) by 1000 , we get */

$\implies 1000x = 1025.\bar{15} \: --(2)$

/* Multiplying equation (2) by 100, we get */

$\implies 100000x = 102515.\bar{15} \: --(3)$

/* Subtract equation (2) from equation (3) , we get*/

$\implies 99000x = 101490$

$\implies x = \frac{101490}{99000}$

$\implies x = \frac{10149}{9900}$

$\implies x = \frac{3383}{3300}\: \blue {[ \frac{p}{q} \: form ]}$

Therefore.,

$\red{1.025\bar{15}}\green { = \frac{3383}{3300}\: \blue {[ \frac{p}{q} \: form ]}}$

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