Question

Find the sum of the first 64 digit of the decimal expansion of 4 by 7

Answer 1

ur ans is 112.2 my dear...
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Answer 2

Answer:

Sum of first 64 digit of the decimal expansion given rational no is 287.

Step-by-step explanation:

we are given $\frac{4}{7}$

To find: sum of first 64 digit of decimal expansion of Given expression.

Since denominator of given rational no. is not factor of 5 or 2 , so the decimal expansion of this rational no is Non Terminating but Repeating.

By dividing 4 by 7 we get following repeating decimal expansion,

$0.571428571428..=0.\overline{571428}$

There are 6 digits in repeation .i.e., 5 , 1 , 7 , 4 , 2 , 8

⇒ among 64 digit 10 times all digits repeat and for left 4 digits only 5 , 7 , 1 , 4 comes.

Thus, in first 64 digit 5 , 7 , 1 , 4 repeats 11 times and 2 , 8 repeats 10 times

So, Sum of first 64 digits = 5 × 11 + 7 × 11 + 1 × 11 + 4 × 11 + 2 × 10 + 8 × 10

                                         = 55 + 77 +1 1 + 44 + 20 + 80

                                         = 287

Therefore, Sum  of first 64 digit of the decimal expansion given rational no is 287.