Problem 52 - Algebra 2

Question

Find each percent. 95% of 500

Step-by-Step Solution

Answer

95% of 500 is 475.

Step 1: Convert Percent to Decimal

To find 95% of a number, first convert the percent into a decimal. Divide 95 by 100. \[ 95\% = \frac{95}{100} = 0.95 \]

Step 2: Multiply by the Decimal

Now, multiply the decimal form of the percent by the number (500).\[ 0.95 \times 500 = 475 \]

Step 3: Interpret the Result

The result from the multiplication is 475, which means that 95% of 500 is 475.

Key Concepts

Converting Percent to Decimal

When you encounter a percent, the first thing you need to do is transform it into a decimal. This makes it much easier for calculations. To convert a percent to a decimal, simply divide the percentage value by 100. This works because percents are based on a whole that is divided into 100 parts. For example, if you have 95%, you would divide by 100 like this:

• Write down the percent: 95%
• Divide by 100: \( \frac{95}{100} = 0.95 \)

Now, 95% is expressed as 0.95 in decimal form.
Doing this conversion lets you handle percentages in mathematical equations just like other numbers. It simplifies the operation that follows, whether it be addition, subtraction, multiplication, or division.

Multiplying Decimals

Once you have converted the percent into a decimal, the next step is to use that decimal in your calculations. Here, you need to multiply the decimal version of the percent by the number you want to find the percent of. This is where multiplying decimals comes into play.

• Take your decimal: 0.95
• Multiply it by the number: 500

Carrying out the multiplication, you'll compute:

• \( 0.95 \times 500 = 475 \)

Always line up the numbers correctly by their far-right digit to avoid errors in decimal placement. This step might look like a standard multiplication, but don't forget to count the decimal places to ensure your answer maintains the correct number of significant digits.
Multiplying with decimals follows the same rules as whole numbers, but you'll adjust at the end to make sure the decimal is placed correctly in your answer.

Interpreting Results

After finishing your calculations, it's crucial to interpret what the numbers represent in the context of your problem. You have determined that 95% of 500 equals 475. This result means that if you have a whole amount of 500, 95% of that total is 475.

• This representation is helpful in understanding quantities like discounts, tax calculations, and proportions.
• It shows how much a percentage actually equates to in real numbers for a given whole amount.

In this example:

• If you had 500 apples, 95% of them, or 475 apples, might be in good condition.
• Similarly, in a financial context, if your savings account total is 500 dollars, earning 95% interest would add 475 dollars to your account.

Interpreting results allows you to give real-world meaning to abstract calculations, helping you to fully grasp and apply the value of percentages in everyday situations.