Question

What is the 217th digit after the decimal point in the repeating decimal 0.3456? How can i calculate this?

Answer 1

Well I think you mean $0.(3456)$, I will try to explain as simple as I can ;p

First I would divide 217 by 4, because we need to find 217th digit in 4 digit repeating decimal:

$217/4=\frac{217}{4}=54\frac{1}{4}$

$54\frac{1}{4}$ it means that 3456 will be reapeted 54 times untill 217th digit, and $\frac{1}{4}$ means that the 217th digit will be the first of those 4 digits in this decimal, so your answer is:
The 217th number after the decimal point in this repeating decimal will be 3