11.11 is what percent of 10 - 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 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, so we can write it down as 100%=10.
4. We know, that x% equals 11.11 of the output value, so we can write it down as x%=11.11.
5. Now we have two simple equations:
1) 100%=10
2) x%=11.11
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%=10/11.11
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 11.11 is what percent of 10

100%/x%=10/11.11
(100/x)*x=(10/11.11)*x       - we multiply both sides of the equation by x
100=0.9000900090009*x       - we divide both sides of the equation by (0.9000900090009) to get x
100/0.9000900090009=x
111.1=x
x=111.1

now we have:
11.11 is 111.1% of 10