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The simplest form of $3. 1416 ¯$ is ____.

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Detailed Solution

The simplest form of

3. 1416 ¯

104719999

.
To express

3. 1416 ¯

in the form of

p q

, assume this number as, say x, and it can be written in the expanded form as follows,

x = 3 ⋅ 141614161416.......

……….. (i)
To shift the decimal point by four places to the right, we multiply the equation (i) by 10000 on each side as follows,

10000 x = 31416 ⋅ 14161416.....

…………. (ii)
Now, subtract equation (i) from (ii) and simplify as follows,

10000 x − x = 31416.14161416..... − 3.14161416..... 9999 x = 31413 x = 314139999 x = 104719999

So, from the above result, we can conclude that,

3. 1416 ¯ = 104719999

.
So, it is the required simplest form.

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