Any decimal whole number can be written as a whole number multiplied by a power of 10. For example,
3 = 3 × 10⁰
100 = 1 × 10²
15,000 = 15 × 10³
The power of 10 that you need depends on how many trailing zeroes you want to remove.
A number with a decimal point can be written the same way, but the power of 10 is negative:
0.3 = 3 × 10⁻¹
0.01 = 1 × 10⁻²
12.345 = 12,345 × 10⁻³
You can employ this sort of manipulation when you're dividing two real numbers. You end up with the quotient of two whole number, and you just need to keep track of power of 10 you end up with.
For example, consider the fraction
1.23 / 0.456
Rewrite this as
(123 × 10⁻²) / (456 × 10⁻³) = 123/456 × 10¹
where we end up with 10¹ because 10⁻²/10⁻³ = 10⁻²⁻⁽⁻³⁾ = 10³⁻² = 10¹.
Now just compute the quotient 123/456 and multiply that result by 10, which amounts to shifting the decimal point one position to the right. You would end up with
123/456 ≈ 0.269737
so that
1.23 / 0.456 ≈ 2.69737
