Problem 27 - Prealgebra

Question

Find the discount to the nearest cent. \(\$ 489\) stereo, \(15 \%\) off

Step-by-Step Solution

Answer

The discount is \(\$73.35\).

Step 1: Understand the Problem

We need to find the amount of money that is being discounted from the original price of a stereo that costs \(\$489\) with a \(15\%\) discount. This means calculating how much \(15\%\) of \(489\) dollars is.

Step 2: Convert the Percentage to a Decimal

To find the discount, start by converting the percentage rate to a decimal. \(15\%\) as a decimal is calculated by dividing \(15\) by \(100\), which gives us \(0.15\).

Step 3: Calculate the Discount Amount

Multiply the decimal form of the percentage by the original price of the stereo to find the discount amount. Thus, \(0.15 \times 489\).

Step 4: Perform the Multiplication

Calculate the product of \(0.15\) and \(489\): \[ 0.15 \times 489 = 73.35 \]This means the discount amount is \(\$73.35\).

Step 5: Round to the Nearest Cent

Checking the result, it's already rounded to the nearest cent as it ends in two decimal places: \(\$73.35\).

Key Concepts

Percentage

Understanding percentages is fundamental to calculating discounts. A percentage represents a portion out of 100. When you see something like a 15% discount, it means you save 15 out of every 100 units of currency.

• The symbol '%' signifies 'percent'.
• Percentages make complex comparisons simple.

For example, if you need to calculate how much 15% of a number is, think of it as 15 per 100. This visualization helps when tackling real-world problems like the discount of a stereo.

Decimal Conversion

Converting a percentage into a decimal is an essential step in most calculations involving percentages. This conversion makes it easier to perform mathematical operations. To convert, simply divide the percentage by 100.

• For example, to convert 15% into a decimal, divide 15 by 100.
• This results in 0.15.

Why do we divide by 100? It stems from the notion that percentages are parts of 100. This conversion lays the groundwork for multiplication and other operations needed to calculate exact values.

Multiplication

Once you have the decimal, the next step is straightforward: multiply. Multiplication is used here to find the actual discount amount from the original price. With the decimal form, you multiply it by the price of the item.

• In our stereo example: multiply 0.15 by $489.
• The product is $73.35.

This result shows you the discount amount. Multiplying with decimals might seem tricky, but it's just regular multiplication followed by counting decimal places.

Rounding to the Nearest Cent

Rounding is essential in ensuring your calculations match practical, everyday transactions. Most currencies need rounding to two decimal places. After your calculation, you may need to round the result to the nearest cent.

• Look at the third decimal place to decide.
• If it's 5 or more, round up.
• If it's less than 5, keep the decimal as is.

In our example: $73.35 was already perfectly rounded as it had two decimal places. Remember, using rounding ensures your answers are usable in real-world scenarios, like purchasing a stereo.