Competition problem — Algebra — Maths Olympiad Prep

Algebra Difficulty 2.1 Junior Find the answer South Africa

$1 \div 13$ is a recurring decimal that begins $0.076923076923076923\ldots$ . The 100th digit after the decimal comma is

Pick one

Solution

There are $6$ digits in the repeating part of the decimal form. $100 = 6 \times 16 + 4$ , so the $100$ th digit will be the $4$ th in the repeating part $076923$ , which is $9$ .

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: MathNet, licensed CC-BY-4.0. Statement and solution reproduced as published; topic and difficulty added by this site.