0.4 is what percent of 45 - 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 45 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 45, so we can write it down as 100%=45.
4. We know, that x% equals 0.4 of the output value, so we can write it down as x%=0.4.
5. Now we have two simple equations:
1) 100%=45
2) x%=0.4
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%=45/0.4
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 0.4 is what percent of 45

100%/x%=45/0.4
(100/x)*x=(45/0.4)*x       - we multiply both sides of the equation by x
100=112.5*x       - we divide both sides of the equation by (112.5) to get x
100/112.5=x
0.88888888888889=x
x=0.88888888888889

now we have:
0.4 is 0.88888888888889% of 45