Question

0. Express 3.67878.... in p/q form.​

Answer 1

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Answer 2

$\huge\underline{\underline{\maltese\:\:\textbf{\textsf{Solution}}}}$

$\sf{\bold Let \: x = 3.67878 ----(i)}$

$\sf{\bold Multiply \: (i) \: by \: 10}$

$\sf{\bold 36.7878 = 10x ----(ii)}$

$\sf{\bold Multiply \: (ii) \: by \: 1000}$

$\sf{\bold 3678.78 = 1000x ----(iii)}$

Then, subtract (iii) -(ii)

$\sf{\bold 1000x-10x = 3678.78-36.7878}$

$\sf{\bold 990x = 3642}$

$\sf{\bold x = \frac{3642}{990} }$

$\sf{\bold x = \frac{37}{165} }$

Hence, it is in P/q form..