Question

express 1.2345 where 45 are bar and express then in p/q form ​

Answer 1

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Answer 2

Let the given number 1.2345 where 45 is overlined, be x.

First we have to multiply this number by 100 such that there will only be 45 overlined (or 45 recurring) after the decimal point.

Then, as 45 is a two digit number, we have to calculate 100 times this obtained number, i.e., 10000x.

Difference of 100x from 10000x gives an integer at RHS due to the cancelling of 45 overlined, thus we can find the answer.

Method is given below:

$\Longrightarrow\ x=1.23\overline{45}\\ \\ \\ \Longrightarrow\ 100x = 1.23\overline{45} \times 100\\ \\ \Longrightarrow\ 100x = 123.\overline{45}\ \ \ \ \ \longrightarrow\ \ \ (1) \\ \\ \\ \Longrightarrow\ 10000x=1.23\overline{45}\times 10000\\ \\ \Longrightarrow\ 10000x = 12345.\overline{45}\ \ \ \ \ \longrightarrow\ \ \ (2)$

$\displaystyle (2) - (1) \\ \\ \\ \Longrightarrow\ 10000x - 100x = 12345.\overline{45} - 123.\overline{45}\\ \\ \\ \Longrightarrow\ 9900x = 12222 \\ \\ \\ \Longrightarrow\ x=\frac{12222}{9900} \\ \\ \\ \Longrightarrow\ \large x = \frac{679}{550}$

Thus the number is written in fractional form, hence we got the answer.