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

Suppose you have some repeating decimal like

x = 0.123123123...

The repeating part has a length of 3, and multiplying both sides by 10^3 = 1000 gives

1000x = 123.123123123...

The usefulness of this is that we can subtract x from this to eliminate the decimal part:

1000x - x = 123.123... - 0.123...

999x = 123

then solve for x as a fraction:

x = 123/999

and in this case the fraction reduces further to

x = 41/333

let's solve your equation step-by-step.

24−3x=−27

step 1: simplify both sides of the equation.

24−3x=−27

24+−3x=−27

−3x+24=−27

step 2: subtract 24 from both sides.

−3x+24−24=−27−24

−3x=−51

step 3: divide both sides by -3.

−3x

−3

=

−51

−3

x=17

answer:

x=17

step-by-step explanation:

mark brainliest and have a great day!