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.