0.707 is what percent of 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 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 1, so we can write it down as 100%=1.
4. We know, that x% equals 0.707 of the output value, so we can write it down as x%=0.707.
5. Now we have two simple equations:
1) 100%=1
2) x%=0.707
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%=1/0.707
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 0.707 is what percent of 1

100%/x%=1/0.707
(100/x)*x=(1/0.707)*x       - we multiply both sides of the equation by x
100=1.4144271570014*x       - we divide both sides of the equation by (1.4144271570014) to get x
100/1.4144271570014=x
70.7=x
x=70.7

now we have:
0.707 is 70.7% of 1