#### Solution for 100.5 is what percent of 40:

100.5:40*100 =

(100.5*100):40 =

10050:40 = 251.25

**Now we have: 100.5 is what percent of 40 = 251.25**

**Question: 100.5 is what percent of 40?**

Percentage solution with steps:

Step 1: We make the assumption that 40 is 100% since it is our output value.

Step 2: We next represent the value we seek with {x}.

Step 3: From step 1, it follows that {100\%}={40}.

Step 4: In the same vein, {x\%}={100.5}.

Step 5: This gives us a pair of simple equations:

{100\%}={40}(1).

{x\%}={100.5}(2).

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS

(left hand side) of both equations have the same unit (%); we have

\frac{100\%}{x\%}=\frac{40}{100.5}

Step 7: Taking the inverse (or reciprocal) of both sides yields

\frac{x\%}{100\%}=\frac{100.5}{40}

\Rightarrow{x} = {251.25\%}

Therefore, {100.5} is {251.25\%} of {40}.

#### Solution for 40 is what percent of 100.5:

40:100.5*100 =

(40*100):100.5 =

4000:100.5 = 39.800995024876

**Now we have: 40 is what percent of 100.5 = 39.800995024876**

**Question: 40 is what percent of 100.5?**

Percentage solution with steps:

Step 1: We make the assumption that 100.5 is 100% since it is our output value.

Step 2: We next represent the value we seek with {x}.

Step 3: From step 1, it follows that {100\%}={100.5}.

Step 4: In the same vein, {x\%}={40}.

Step 5: This gives us a pair of simple equations:

{100\%}={100.5}(1).

{x\%}={40}(2).

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS

(left hand side) of both equations have the same unit (%); we have

\frac{100\%}{x\%}=\frac{100.5}{40}

Step 7: Taking the inverse (or reciprocal) of both sides yields

\frac{x\%}{100\%}=\frac{40}{100.5}

\Rightarrow{x} = {39.800995024876\%}

Therefore, {40} is {39.800995024876\%} of {100.5}.

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