Question

Express 4 127127127.... in the form p/q , where p and q are integers and q is not equal to 0

Answer 1

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⠀

⠀Let x = 4.127127127... ____(1)⠀

Multiply equation (1) with 1000,we get

1000x = 4127.127127127... ____(2)

Now, subtract equation (1) from equation (2)

1000x - x = 4127.127127127... - 4.127127127...⠀

⟹ 999x = 4123

$⟹ \: x = \frac{4123}{999}$

Hence, 4.127127127... can be written as 4123/999 in the form of p/q, where p and q are integers and q is not equal to 0.