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Digit in a Large Integer

Q34 WK9 II: Let n be the largest integer for which 14n has exactly 100 digits. Counting from right to left, what is the 68th digit of n?

Solution

Largest 100 digit number is 99999999....repeated to 100 digits

    14n = 999999...100 digits
    => n = 99999...100 digits / 14
    => n = 7142857142714285714285...upto 99 (100 − 1) digits

Now, the 68th digit from right of a 99 digit number is the same as 99 − 68 + 1 = 32nd digit from left of the number.

Since n = repetition of a group of 6 digits 714285, the 32nd digit is the 2nd digit in 714285, which is 1.