Problem 23 - Prealgebra

Question

The following problems are similar to Problems \(1-22\). Set them up in the same way, but use a calculator for the calculations. Sales Tax The sales tax rate on a certain item is \(5.5 \%\). If the purchase price is \(\$ 216.95\), how much is the sales tax? (Round to the nearest cent.)

Step-by-Step Solution

Answer

The sales tax is \( \$11.93 \).

Step 1: Understand the Problem

We are given a purchase price of \( \$216.95 \) and a sales tax rate of \( 5.5\% \). Our goal is to calculate the amount of sales tax that needs to be added to the purchase price.

Step 2: Convert the Tax Rate to a Decimal

To use the sales tax rate in calculations, convert it from a percentage to a decimal. Divide \( 5.5 \% \) by \( 100 \) to get \( 0.055 \).

Step 3: Calculate the Sales Tax

Multiply the purchase price by the decimal sales tax rate to find the amount of sales tax:\[\\(216.95 \times 0.055 = \\)11.93225\]

Step 4: Round to the Nearest Cent

Round the sales tax to the nearest cent. The calculated sales tax is \( \\(11.93225 \), which rounds to \( \\)11.93 \).

Key Concepts

Sales Tax Calculation

Calculating sales tax is crucial when shopping, as it determines the extra amount you need to pay on top of an item's purchase price. To find the sales tax, you first need two key pieces of information: the sales tax rate and the purchase price. The sales tax rate is usually given as a percentage, like in our example where it's \(5.5\%\). To use this percentage in calculations, you must convert it into a decimal. This is done by dividing the percentage by 100. For instance, \(5.5\%\) becomes \(0.055\).
Once converted, you simply multiply this decimal by the purchase price to find the sales tax amount. In our example, with a purchase price of \(\$216.95\), the calculation looks like this:

• Convert: \(5.5\% = 0.055\)
• Multiply: \(216.95 \times 0.055 = 11.93225\)

After computing the multiplication, you will arrive at the unrounded sales tax amount. It's crucial to know that some sales taxes could have different percentages depending on your location, so always use the correct rate for accurate calculations.

Using a Calculator

Using a calculator is a valuable skill, especially when dealing with large numbers or precise decimals. In the case of calculating sales tax, a calculator helps ensure accuracy and saves time. To calculate sales tax using a calculator, follow these uncomplicated steps:

• Begin by entering the purchase price, in this case, \(\$216.95\).
• Next, multiply by the decimal sales tax rate. Press the multiplication (\(*\)) key, followed by typing \(0.055\) for \(5.5\%\).
• Finish by hitting the equals (=) key to see the result, which in this example is \(11.93225\).

Using a calculator reduces the possibility of making simple arithmetic errors, especially with decimal places. It's important, however, to double-check your inputs. Ensure the correct numbers are used to avoid incorrect results. Therefore, mastering the use of a calculator for percentage calculations like sales tax can be a significant time-saver and provide peace of mind.

Rounding to Nearest Cent

Rounding to the nearest cent is an important step after calculating a figure like sales tax. This is because currency is usually expressed to two decimal places. Once you have your calculated sales tax, which in this instance is \(11.93225\), you need to round it correctly.To round to the nearest cent, you should focus on the third decimal place:

• If it is 5 or higher, round the second decimal place up. For example, 11.932 becomes \(11.93\) by rounding up.
• If it's less than 5, you simply drop the remaining decimals without changing the second decimal place.

In this scenario, since the third decimal in \(11.93225\) is greater than 5, you round up from \(11.93\). Rounding ensures that your financial calculations are precise and practical, making transactions or budget considerations easier to manage.