What is 100.0001 percent of 166 - 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 166 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 166 is 100%, so we can write it down as 166=100%.
4. We know, that x is 100.0001% of the output value, so we can write it down as x=100.0001%.
5. Now we have two simple equations:
1) 166=100%
2) x=100.0001%
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:
166/x=100%/100.0001%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 100.0001% of 166

166/x=100/100.0001
(166/x)*x=(100/100.0001)*x       - we multiply both sides of the equation by x
166=0.999999000001*x       - we divide both sides of the equation by (0.999999000001) to get x
166/0.999999000001=x
166.000166=x
x=166.000166

now we have:
100.0001% of 166=166.000166