# 46 percent of 100?

### Solution for 'What is 46% of 100?'

In all the following examples consider that:

- The percentage figure is represented by X%
- The whole amount is represented by W
- The portion amount or part is represented by P

#### Solution Steps

The following question is of the type "How much X percent of W", where W is the whole amount and X is the percentage figure or rate".

Let's say that you need to find 46 percent of 100. What are the steps?

Step 1: first determine the value of the whole amount. We assume that the whole amount is 100.

Step 2: determine the percentage, which is 46.

Step 3: Convert the percentage 46% to its decimal form by dividing 46 into 100 to get the decimal number 0.46:

46100 = 0.46

Notice that dividing into 100 is the same as moving the decimal point two places to the left.

46.0 → 4.60 → 0.46

Step 4: Finally, find the portion by multiplying the decimal form, found in the previous step, by the whole amount:

0.46 x 100 = 46 (answer).

The steps above are expressed by the formula:

P = W × X%100

This formula says that:

*"To find the portion or the part from the whole amount, multiply the whole by the percentage, then divide the result by 100"*.

The symbol % means the percentage expressed in a fraction or multiple of one hundred.

Replacing these values in the formula, we get:

P = 100 × 46100 = 100 × 0.46 = 46 (answer)

Therefore, the answer is 46 is 46 percent of 100.

### Solution for '46 is what percent of 100?'

The following question is of the type "P is what percent of W,” where W is the whole amount and P is the portion amount".

The following problem is of the type "calculating the percentage from a whole knowing the part".

#### Solution Steps

As in the previous example, here are the step-by-step solution:

Step 1: first determine the value of the whole amount. We assume that it is 100.

(notice that this corresponds to 100%).Step 2: Remember that we are looking for the percentage 'percentage'.

To solve this question, use the following formula:

X% = 100 × PW

This formula says that:

*"To find the percentage from the whole, knowing the part, divide the part by the whole then multiply the result by 100"*.

This formula is the same as the previous one shown in a different way in order to have percent (%) at left.

Step 3: replacing the values into the formula, we get:

X% = 100 × 46100

X% = 4600100

X% = 46.00 (answer)

So, the answer is 46 is 46.00 percent of 100

### Solution for '100 is 46 percent of what?'

The following problem is of the type "calculating the whole knowing the part and the percentage".

### Solution Steps:

Step 1: first determine the value of the part. We assume that the part is 100.

Step 2: identify the percent, which is 46.

Step 3: use the formula below:

W = 100 × PX%

This formula says that:

*"To find the whole, divide the part by the percentage then multiply the result by 100"*.

This formula is the same as the above rearranged to show the whole at left.

Step 4: plug the values into the formula to get:

W = 100 × 10046

W = 100 × 2.1739130434783

W = 217.39130434783 (answer)

The answer, in plain words, is: 100 is 46% of 217.39130434783.