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Chapter 4: Problem 10

. \(7.454 \times 2.3=\)

Short Answer

Expert verified
The answer is 17.1442.

Step by step solution

01

Multiply Whole Numbers

First, ignore the decimal points and multiply the whole numbers as if they were integers. Multiply 7454 by 23.
02

Calculate the Product

Perform the multiplication: \[ 7454 \times 23 = 171442 \]
03

Adjust for Decimal Places

Now, count the total number of decimal places in the original numbers. 7.454 has 3 decimal places and 2.3 has 1 decimal place, so together they have 4 decimal places.
04

Place the Decimal Point

Adjust the product from step 2 by placing the decimal point in the correct position. Since there are 4 decimal places total, place the decimal point 4 digits from the right in 171442: \[ 171442 \rightarrow 17.1442 \]

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Key Concepts

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

multiplying decimals
Multiplying decimals might seem tricky, but it becomes simple if we follow a structured approach. When we multiply decimals, the essential steps involve first ignoring the decimals altogether. This means treating the numbers as whole numbers. For example, in the problem given: instead of multiplying 7.454 by 2.3 directly, we first treat them as 7454 and 23. This simplifies the multiplication process since you're working with whole numbers.
decimal places
Decimal places are crucial in determining where to place the decimal point in the final result. After you've multiplied the whole numbers, the next step involves counting the total number of decimal places in both original numbers. In our example, 7.454 has 3 decimal places, and 2.3 has 1 decimal place. Together, they make up 4 decimal places. This total count will tell you how many places from the right you must put the decimal point in your product.
step-by-step math solutions
Using a step-by-step approach to solving decimal multiplication problems can demystify the process:

1. **Ignore Decimal Points:** Start by ignoring the decimal points and multiply the numbers as if they were whole numbers. This simplifies the initial multiplication process.

2. **Multiply Whole Numbers:** Using the example, multiply 7454 by 23 to get 171442.

3. **Count and Adjust for Decimal Places:** Add up the total decimal places from both numbers, which in this case is 4. Now, place the decimal point 4 digits from the right in your product to get 17.1442.

By breaking the problem down into these clear steps, handling decimal multiplication becomes straightforward and manageable.

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Most popular questions from this chapter

. Ilya bought 0.460 pounds of meat at \(\$ 5.50\) per pound. How much did the meat cost? A. \(\$ 2.53\) B. \(\$ 5.04\) C. \(\$ 5.96\) D. \(\$ 11.96\)

Alan needs 7 quarters to do his laundry. What is the most he could spend from a \(\$ 20.00\) bill and still have enough left to wash his clothes? A. \(\$ 1.75\) B. \(\$ 2.86\) C. \(\$ 16.75\) D. \(\$ 18.25\)

Peter has a job that pays \(\$ 17.50\) per hour for 40 hours per week, and he is paid each Friday. This week the company deducted \(\$ 44.94\) for Social Security, \(\$ 10.50\) for Medicare, \(\$ 7.00\) for State Disability Insurance, and \(\$ 79.50\) for Income Tax Withholding. What is Peter's take-home pay this week if he has no other deductions? A. \(\$ 141.94\) B. \(\$ 558.06\) C. \(\$ 700.00\) D. \(\$ 841.94\)

\(34.56-13.23=\)

One week Sam worked 32.75 hours at his job, which pays \(\$ 17.50\) per hour. How much did he earn that week before taxes and other deductions? Round to the nearest cent. A. \(\$ 50.25\) B. \(\$ 560.00\) C. \(\$ 573.13\) D. \(\$ 5,731.25\)
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