Question

Why does it work to multiply the divisor and the dividend by the same power of ten (such as 10, 100, 1000) and you still get the same answer as if you were to divide the decimals?

Answer 1

It works because dividing is the opposite of multiplying. An example would be dividing by four and multiplying by 0.25. Division is really just a fraction, as is the other way around. 1 ÷ 4 is the same as
`(1)/(4)`, so dividing decimals is really just multiplying a fraction, which can also be a division problem!