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

We'd like to take a repeating decimal and express it as a quotient of two whole numbers. The idea is to multiply by some number (10, 100, 1000, etc.) so that when we subtract the original number from the multiple, the repeating part cancels out. If we multiply by 10, we get 10x = 2.

Step-by-step explanation:

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.

answer: 1,380

step-by-step explanation:

1: you turn %15 into a decimal by moving the decimal point two places to the left.

2: and then you multiply .15 by 1,200 , which will get you 180.00

3: from there you will add 180 to 1,200

4: which will get you 1,380

hope it *im kind of slow so idk if my answer is right*

a: 1/6, j: 1/4

step-by-step explanation: you are welcome