Question

Sammie put 11.74 gallons of gasoline in her car at a cost of \(\$ 3.459\) per gallon. How much did she pay for the gasoline, rounded to the nearest cent? A. \(\$ 3.39\) B. \(\$ 8.28\) C. \(\$ 40.61\) D. \(\$ 42.00\)

Short answer

C. 40.61

Step-by-step solution

- Identify the given values

Sammie put 11.74 gallons of gasoline in her car. The cost per gallon is \(3.459\) dollars.

- Set up the multiplication

To find the total cost, multiply the number of gallons by the cost per gallon: \(11.74 \text{ gallons} \times 3.459 \text{ dollars per gallon}\).

- Perform the multiplication

Calculate the product: \(11.74 \times 3.459 = 40.58946\).

- Round to the nearest cent

The product calculated is \(40.58946\). To round to the nearest cent, check the third decimal place. If it is 5 or above, round up the second decimal. Hence, \(40.58946 \text{ rounds to } 40.59\).

- Match with given choices

Compare the rounded amount, \(40.59\), with the given options. The closest matching option is C. \(40.61\).

Key concepts

Multiplication

Multiplication is a fundamental arithmetic operation used to calculate the total amount when you have a repeated addition scenario. For example, in this exercise, Sammie filled her car with 11.74 gallons of gasoline, each costing \(3.459 per gallon. To find the total cost, you multiply the number of gallons by the price per gallon:

• Given the values: 11.74 gallons and \)3.459 per gallon
• Set up the multiplication: 11.74 × 3.459
• Calculate the product

Multiplication helps combine multiple identical groups into a single total value. Use a calculator to get 11.74 × 3.459 = 40.58946. This product tells you the total cost before rounding.

Rounding Numbers

Rounding numbers makes them simpler and easier to work with, especially when dealing with money. When you're rounding to the nearest cent, you look at the third decimal place (thousandths place). If this digit is 5 or higher, you round up. If it's 4 or lower, you round down. Here’s how you’d round 40.58946 to the nearest cent:

• Examine the third decimal place: 9
• Since 9 is greater than 5, round up the second decimal place
• So, 40.58946 becomes 40.59

Rounding ensures that financial transactions are accurate and comply with common monetary standards.

Unit Price Calculation

Understanding unit price calculation is essential for making smart purchasing decisions. The unit price tells you the cost per single unit of measure. To find the total price when you buy multiple units, you multiply the unit price by the quantity:

• Identify the unit price: $3.459 per gallon
• Determine the quantity: 11.74 gallons
• Multiply to get the total cost: 11.74 × 3.459 = 40.58946

By calculating the unit price and using it to find the total cost, you ensure an accurate understanding of expenses and budgeting.