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Chapter 1: Problem 63

The sales tax rate in a state is \(6 \%\). Find the sales tax on a purchase of \(\$ 750\).

Short Answer

Expert verified
The sales tax on \$750 is \$45.

Step by step solution

01

Identify the sales tax rate

The sales tax rate provided in the problem is 6%. This means that for every dollar spent, an additional 6% of that dollar is added as tax.
02

Convert the percentage to a decimal

Convert the sales tax rate from a percentage to a decimal by dividing by 100. So, 6% becomes 0.06.
03

Calculate the sales tax amount

Multiply the purchase amount by the decimal sales tax rate. For a purchase of \$750:\[\text{Sales Tax} = 750 \times 0.06 = 45.\]So, the sales tax on a purchase of \$750 is \$45.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Sales Tax Rate
Sales tax is a percentage of the purchase price, which is charged by the government on the goods or services you buy. In our example, the sales tax rate is given as 6%.
This means for every dollar you spend, you need to pay an additional 6 cents as tax. Understanding the sales tax rate is crucial, as it determines how much extra you will pay above the listed price. Often, the rate varies from state to state or country to country, so it's important to know the local rate.
Percentage to Decimal Conversion
Percentages are another way of expressing parts of a whole. To use them in calculations, we convert them to decimal form. Converting a percentage to a decimal is straightforward: divide the percentage by 100.
For example, the sales tax rate of 6% becomes:
\[ 6 \text{%} \bigg/ 100 = 0.06 \]
This decimal format of the percentage helps in performing arithmetic operations like multiplication or division more easily. Always remember, to convert any percentage to a decimal, just divide by 100.
Multiplication of Decimals
Once we have the decimal form of the sales tax rate, the next step is to calculate the amount of sales tax by multiplying this decimal rate by the purchase amount. Here鈥檚 how:
For example, suppose the purchase amount is \$750\$. Given our decimal sales tax rate of \0.06\, we'd compute the sales tax as follows:
\[ \text{Sales Tax} = 750 \times 0.06 = 45 \]
This multiplication tells us that for a purchase of \$750\$, we'll pay \$45\ in sales tax. To multiply decimals:
  • Line up the numbers by their rightmost digits, ignoring the decimal points.
  • Multiply the numbers as if they were whole numbers.
  • Place the decimal point in the result by counting the total number of decimal places in the factors.

In this example, both factors have a total of two decimal places, so the product \45\ correctly places the decimal point after the hundredths place.

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Most popular questions from this chapter

The International Basketball Federation rules (2006) state, "For all men's competitions in all categories, the circumference of the ball shall be no less than \(749 \mathrm{~mm}\) and no more than \(780 \mathrm{~mm}\) (size 7)." Find the maximum volume of the ball in cubic millimeters. Round to the nearest whole number. (Source: www.fiba.com)

Find the circumference of a circle with a diameter of \(13 \mathrm{~cm}\).

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