#### Solution for 8.2 is what percent of 40:

8.2:40*100 =

(8.2*100):40 =

820:40 = 20.5

Now we have: 8.2 is what percent of 40 = 20.5

Question: 8.2 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\%}={8.2}.

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

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

{x\%}={8.2}(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}{8.2}

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

\frac{x\%}{100\%}=\frac{8.2}{40}

\Rightarrow{x} = {20.5\%}

Therefore, {8.2} is {20.5\%} of {40}.

#### Solution for 40 is what percent of 8.2:

40:8.2*100 =

(40*100):8.2 =

4000:8.2 = 487.80487804878

Now we have: 40 is what percent of 8.2 = 487.80487804878

Question: 40 is what percent of 8.2?

Percentage solution with steps:

Step 1: We make the assumption that 8.2 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\%}={8.2}.

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

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

{100\%}={8.2}(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{8.2}{40}

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

\frac{x\%}{100\%}=\frac{40}{8.2}

\Rightarrow{x} = {487.80487804878\%}

Therefore, {40} is {487.80487804878\%} of {8.2}.

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