Math Help Please

OK, IM guessing this is from AoPS from the dollar signs...... I don't really mind the asking and I would solve it but can you edit it so the latex is in latex???????? ok so this is my version of it...:

1.) Find the first ten digits after the decimal point in the decimal expansion of $\frac{10}{27}=0.abcdefghij\ldots$

 without a calculator.

(Express your answer as a ten-digit number.)

2.) The number $\frac{12}{13}$ can be expressed as a repeating decimal $0.\overline{abcdef}$. Find the repeating part $abcdef$ without a calculator.

3.) Convert $0.04\overline{55}$ to a fraction in simplest form.

4.) Convert $6032_8$ to decimal.

5.) Convert $999_{16}$ to decimal.

6.) Convert 35 from base 10 to base 2.

(You do not need to include the subscript 2 in this answer.)

7.) Convert $2231_4$ to base 2 without first converting to decimal.

1) $\dfrac{10}{27} = \dfrac{370}{999} = 0.\overline{370} = 0.370\;370\;370\;3...$

2) $\dfrac{12}{13} = \dfrac{923076}{999999} = 0.\overline{923076}$

3) 

$\quad0.04\overline{55}\\ = 0.04 + 0.00\overline{5}\\ = \dfrac{4}{100} + \dfrac{0.\overline{5}}{100}\\ = \dfrac{4}{100} + \dfrac{5}{900}\\ = \dfrac{41}{900}$

4)

$\quad 6032_8\\ = 6\cdot 8^3 + 3\cdot 8 + 2\\ = 3098$

5)

$\quad 999_{16}\\ = 9(16^2 + 16 + 1)\\ = 2457$

6)

$35 = 2^5 + 2^1 + 2^0\\ 35 = 100011_2$

7)

$\quad 2231_4\\ = 10101101_2$