Question

Solve the percent problem. 100 is \(1 \%\) of what number?

Short answer

The number we are looking for is 10,000.

Step-by-step solution

Express Percent as Decimal

First, you need to convert the percentage into a decimal. This can be done by dividing the percentage by 100. So, \( 1 \% = \frac{1}{100} = 0.01 \).

Use Percentage Equation

Next, you can put the known values into the percentage equation. Our equation is \( \frac{100}{?} = 0.01 \). The question mark represents the number we are trying to find (the whole).

Solve for Unknown

To isolate the unknown on one side of the equation, you should multiply each side of the equation by this unknown (?). This gives you \( 100 = ? \times 0.01 \). Then, to solve for ?, you should divide each side of the equation by 0.01. This gives you \( \frac{100}{0.01} = ?\).

Calculate Result

Calculate the result of dividing 100 by 0.01. This gives you \( ? = 10,000 \).

Key concepts

Percent to Decimal Conversion

Understanding how to convert a percentage to a decimal is a foundational skill required for solving percent problems. Why is this conversion important? Because it simplifies math operations and prepares the percentage to be easily manipulated in equations. Let's delve into the process:

To convert a percentage to a decimal, simply divide the percentage by 100. This is because 'percent' literally means 'per hundred', implying that the value is calculated out of a total of 100. So, when you're faced with a problem that states something like '1%', you convert this to a decimal by doing the division: \( 1\% = \frac{1}{100} = 0.01 \).

This step paves the way to using this decimal in various mathematical operations, such as multiplication and division, to solve the problem at hand. Remember, decimal numbers are much easier to work with, especially when you're using calculators or doing mental math.

Percentage Equation

Once the percent is converted to a decimal, the next step involves putting this value into the percentage equation. What exactly is a percentage equation? It's an expression that helps you find out 'what percentage one number is of another' or, as in our exercise, 'what is the total if a part and its percentage of the total are known'.

In general terms, the percentage equation can be written as: \( \frac{part}{whole} = percentage\ as\ decimal \) where the 'part' is the portion of the whole amount, the 'percentage as decimal' is your converted percent value, and the 'whole' is what you're trying to find out.

In the exercise, we're trying to find the whole when we know that 100 is 1% of it. Using the percentage equation, this would look like: \( \frac{100}{?} = 0.01 \) where '?' represents what we are solving for. Setting up the equation correctly is crucial as it directs us towards the solution.

Isolating the Unknown

Often in math problems, we are required to find an unknown value. In percentage problems, isolating the unknown is key to finding your answer. How do we do this? By rearranging the equation so that the unknown we're looking for is alone on one side.

In the provided exercise, we've got our percentage equation set up as \( \frac{100}{?} = 0.01 \), and we want to isolate the '?'. To achieve this, we need to eliminate the fraction by multiplying both sides of the equation by '?', which yields: \( 100 = ? \times 0.01 \). To get '?' by itself, we then divide both sides of the equation by 0.01. We end up with \( ? = \frac{100}{0.01} \).

When you isolate the unknown successfully, the path forward becomes clear, and you only need to perform the arithmetic operation to find the number you're looking for. In our problem, this final step reveals that the unknown whole is 10,000, completing the solution to the percent problem.