Why do you multiply by a power of 10 when writing a repeating decimal as a rational number

1.28 = 128 * 10^-2

128 * (1/10^2)

128 / 10^2

128 / 100

1.28

Because, it's literally the same thing mathematically if you worked it out. Though, as I'm sure you're aware, it's just a much shorter and cleaner way of writing out large or small numbers.

B. 2 1/2 feet. multiply 2.5 inches by 12 to get thirty inches then divide by 12 to get 2.5 feet