36.6666666667 is what percent of 360 - 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 360 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 360, so we can write it down as 100%=360.
4. We know, that x% equals 36.6666666667 of the output value, so we can write it down as x%=36.6666666667.
5. Now we have two simple equations:
1) 100%=360
2) x%=36.6666666667
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%=360/36.6666666667
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 36.6666666667 is what percent of 360

100%/x%=360/36.6666666667
(100/x)*x=(360/36.6666666667)*x       - we multiply both sides of the equation by x
100=9.8181818181729*x       - we divide both sides of the equation by (9.8181818181729) to get x
100/9.8181818181729=x
10.185185185194=x
x=10.185185185194

now we have:
36.6666666667 is 10.185185185194% of 360