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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

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. \(\$ 42.00\)

On the number line, what is the distance between -1.45 and -8.34 ? A. -9.79 B. -6.89 C. 6.89 D. 9.79

It is roughly \(93,000,000\) miles from Earth to the sun. A scientist would express this number as A. \(93,000,000\) miles. B. \(93 \times 10^6\) miles. C. \(9.3 \times 10^7\) miles. D. \(0.0093 \times 10^9\) miles.

Ken Johnson's place is located 17.35 kilometers due west of the center of town on Route 17. Willy Hester's place is located 11.23 kilometers due west of the center of town, also on Route 17. How far from each other do the two neighbors live? A. 6.12 kilometers B. 14.28 kilometers C. 28.58 kilometers D. 45.58 kilometers

Tony fills his car with gas. His tank holds 14.0 gallons of gas. He pumps 8.37 gallons into the tank. If his car averages 27.6 miles per gallon, how far could he have driven before running out of gas had he not stopped to fill up? Give your answer to the nearest whole mile. A. 155 miles B. 386 miles C. 462 miles D. 617 miles
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