Integers..find the values of x and y?

Question

The number 3002.05 can be written as 3 * 10^3 + 2 * 10^ (x) + 5 * 10^(y).

Given that x and y are integers, find the values of x and y.

ans is x = 0, y = -2

Please show me your workings clearly pls..thks

Answer 1

2 = 2*10^x 10^0 = 1 so x = 0
and 0.05 = 5*0.01 = 5 * 10 (-2) so y = -2

Answer 2

3002.05 = 3000 + 2 + 0.05

3000 = 3*10³
2 = 2*10^x ⇒ 10^x = 1 ⇒ x = 0
0.05 = 5*10^y ⇒ 10^y = .01 ⇒ y = -2

Answer 3

3 * 10^3 = 3000

We want 2 * 10^x = 2

So x = 0 because 2 * 10^0 = 2 * 1 = 2

Now we need 5 * 10^y = .05

y = -2 because 10^(-2) = .01 and 5 * .01 = .05

You could also know it is 5 * 10^(-2) because 10^(-2) means move the decimal place in 5. two places left which is .05