A. Decimal expansions and repeating fractions Verify these decimal expansions:

A. Decimal expansions and repeating fractions

Verify these decimal expansions:

1/3 = 0.(3)

1/6 = 0.1(6)

7/30 = 0.2(3)

7/11 = 0.(63)

Find the 100th digit after the decimal point in the expansion of 1/7.

Division by strings of 9s; purely periodic fractions:

Compute by long division: 1 ÷ 9; 1 ÷ 99; 1 ÷ 9,999.

Prove the general rule: 1/(99…9) = 0,(00…01), where the denominator has n nines and the repeating block has length n with (n−1) zeros followed by