Find the first ten digits after the decimal point in the decimal expansion of \frac{13}{29}=0.abcdefghij\ldots without a calculator.

Question

(Express your answer as a ten digit number.)

Answer 1

First, we can convert the fraction $\frac{13}{29}$ into a decimal by performing long division:

$29 | 130.0000000000$
$-116$
$140$
$-116$
$240$
$-232$
$80$
$-58$
$220$
$-232$
$1110$

This process tells us that $\frac{13}{29} = 0.\overline{448275862}$

Therefore, the first ten digits after the decimal point are $\boxed{4482758620}$.