Question

If sales tax is 6 percent, what would be the tax on a shirt that cost \(\$ 68.30\) ? Round your answer to the nearest cent. (A) \(\$ 4.09\) (B) \(\$ 4.10\) (C) \(\$ 4.58\) (D) \(\$ 4.59\)

Short answer

The correct answer is (B) $4.10.

Step-by-step solution

Convert the percentage to a decimal

To convert the percentage to a decimal, divide the percentage by 100. In this case, the sales tax is 6%, so we will divide 6 by 100. 6% ÷ 100 = 0.06

Calculate the tax amount

Now, we will multiply the cost of the shirt ($68.30) by the decimal representation of the sales tax rate (0.06): Tax amount = Cost of shirt × Sales tax rate Tax amount = $68.30 × 0.06

Perform the multiplication

Next, we will multiply 68.30 by 0.06: \(68.30 × 0.06 = 4.098\)

Round the tax amount

Now, we will round the tax amount (4.098) to the nearest cent: Tax amount = $4.10 (rounded to the nearest cent)

Identify the correct answer choice

Finally, we will compare our rounded tax amount to the given answer choices and select the correct one: The correct answer is (B) $4.10.

Key concepts

Percentage to Decimal Conversion

When calculating sales tax, the first step is converting the percentage rate into a decimal. This conversion is essential, as it transforms the percentage into a form that can be used directly in calculations. To do this, you simply divide the percentage by 100. For example, if the sales tax is 6%, divide 6 by 100 to get 0.06.

• Take the percentage value, here it's 6%.
• Divide by 100: 6 ÷ 100.
• This results in 0.06, which is the decimal form of 6%.

Converting percentages to decimals simplifies calculation because working directly with decimals allows for straightforward arithmetic operations, like multiplication, necessary for finding sales tax costs.

Multiplication of Decimals

After converting the percentage to a decimal, the next step is to calculate the sales tax amount. This involves multiplying the item's price by the decimal form of the sales tax rate. Let’s see how this works with our shirt example:

• The shirt costs $68.30.
• The decimal form of the sales tax is 0.06.

To find the tax, multiply these two values:\[ 68.30 \times 0.06 = 4.098 \]Remember that when multiplying decimals, the number of decimal places in the result is the sum of the decimal places in the numbers being multiplied. Thus, the precise calculation here becomes crucial to understanding exactly how the tax amount evolves directly from the initial figures.

Rounding to Nearest Cent

Once the multiplication is complete, you have a precise decimal result—in this case, 4.098. However, in most practical scenarios, particularly financial ones, results need to be expressed in terms of currency, which often means rounding to the nearest cent. Let’s explore how this rounding is done:

• Identify the third decimal place: in 4.098, it’s 8.
• If the third digit is 5 or greater, increase the second digit by one. Here, 8 is more than 5.
• Thus, the result 4.098 becomes rounded to 4.10.

Rounding ensures clarity and precision in accounting, where many transactions need to be handled to exact cents, particularly for sales tax calculations where numerous such transactions aggregate.