The decimal expansion of 1/13 is 0.076923076923…, repeating the block 076923. What is the sum of its first 20 digits after the decimal point?

Learn / Library / Mental math

Digit sum of a long expansion

Mental mathHard

The decimal expansion of $\frac{1}{13}$ is $0.076923076923 \dots$ , repeating the block $076923$ . What is the sum of its first $20$ digits after the decimal point?

Checking an answer needs JavaScript. The hint and the solution open without it.

Hint

Add up one full block, then deal with the leftover digits.

Solution

One block has digit sum $0 + 7 + 6 + 9 + 2 + 3 = 27$ .
$20 = 6 \times 3 + 2$ , so there are $3$ full blocks and $2$ extra digits.
The blocks give $3 \times 27 = 81$ , and the extra digits $0$ and $7$ give $7$ .
The total is $81 + 7 = 88$ .

Answer: $88$

Next question Back to the library