Problem 63
Question
The sales tax rate in a state is \(6 \%\). Find the sales tax on a purchase of \(\$ 750\).
Step-by-Step Solution
Verified Answer
The sales tax on \$750 is \$45.
1Step 1: 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.
2Step 2: 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.
3Step 3: 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.
Key Concepts
Sales Tax RatePercentage to Decimal ConversionMultiplication of Decimals
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.
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.
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’s 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:
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.
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.