Question

1.Represent 3.5373737..... in p/q form where p and q are aintegers and q≠0.

Answer 1

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☞ $\sf x=\dfrac{35020}{9900}$

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✭ 3.5373737.....

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◈ Its p/q form?

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So to represent a number in its p/q we have to convet the decimal number into a fraction where p & q are Integers and q ≠ 0

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Here we are given 3.5373737..... In it we may observe that 73 is recurring and the rest, that is 3.53 is not ,so we shall subtract 737373... from the number

➝ $\sf x = 3.53737373...$

➝ $\sf 10000x = 3.53737373\dots ×\times10000$

➝ $\sf 1000x = 35373.7373... \:\:\: -eq(1)$

Similarly,

➝ $\sf 100x = 3.537373... \times 00$

➝ $\sf 100x = 353.7373... \:\:\: -eq(2)$

Subtracting eq(2) from eq(1)

➳ $\sf 10000x-100x = 35373.7373..$

➳ $\sf 9900x = 35020$

➳ $\sf \orange{x=\dfrac{35020}{9900}}$

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Answer 2

Hello Dear User, Hope you are doing good

Question :-

Represent 3.5373737..... in p/q form where p and q are integers and q≠0.

Answer :

Explanation :-

Let 3.5373737.... be "x"

Then x = 3.5373737....

From this :

1000 x = 1000 * 3.5373737....

1000 x = 3537.3737....              (1)

Now :

500 x = 500 * 3.5373737....

500 x = 1768.68685....             (2)

Now follow this method :

(1) - (2)

1000 x - 500 x =  1768.68685..

500 x =  1768.68685..