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.

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950