0.9 is what percent of 1.01 - 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 1.01 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 1.01, so we can write it down as 100%=1.01.
4. We know, that x% equals 0.9 of the output value, so we can write it down as x%=0.9.
5. Now we have two simple equations:
1) 100%=1.01
2) x%=0.9
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%=1.01/0.9
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 0.9 is what percent of 1.01

100%/x%=1.01/0.9
(100/x)*x=(1.01/0.9)*x       - we multiply both sides of the equation by x
100=1.1222222222222*x       - we divide both sides of the equation by (1.1222222222222) to get x
100/1.1222222222222=x
89.108910891089=x
x=89.108910891089

now we have:
0.9 is 89.108910891089% of 1.01