9.9 is what percent of 10.1 - 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 10.1 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 10.1, so we can write it down as 100%=10.1.
4. We know, that x% equals 9.9 of the output value, so we can write it down as x%=9.9.
5. Now we have two simple equations:
1) 100%=10.1
2) x%=9.9
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%=10.1/9.9
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 9.9 is what percent of 10.1

100%/x%=10.1/9.9
(100/x)*x=(10.1/9.9)*x       - we multiply both sides of the equation by x
100=1.020202020202*x       - we divide both sides of the equation by (1.020202020202) to get x
100/1.020202020202=x
98.019801980198=x
x=98.019801980198

now we have:
9.9 is 98.019801980198% of 10.1