99.9 is what percent of 10.2 - step by step solution

To get the solution, we are looking for, we need to point out what we know.

1. We assume, that the number 10.2 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 100% equals 10.2, so we can write it down as 100%=10.2.
4. We know, that x% equals 99.9 of the output value, so we can write it down as x%=99.9.
5. Now we have two simple equations:
1) 100%=10.2
2) x%=99.9
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
100%/x%=10.2/99.9
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 99.9 is what percent of 10.2

100%/x%=10.2/99.9
(100/x)*x=(10.2/99.9)*x       - we multiply both sides of the equation by x
100=0.1021021021021*x       - we divide both sides of the equation by (0.1021021021021) to get x
100/0.1021021021021=x
979.41176470588=x
x=979.41176470588

now we have:
99.9 is 979.41176470588% of 10.2