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Chapter 2: Problem 23

Multiply as indicated. 23\. \(0.48 \times 1000\) \\ \hline \end{tabular}

Short Answer

Expert verified
480

Step by step solution

01

- Understand the Problem

Identify that you need to multiply the decimal number 0.48 by 1000.
02

- Apply Multiplication by 1000

To multiply a decimal number by 1000, move the decimal point three places to the right.
03

- Perform the Calculation

Move the decimal point in 0.48 three places to the right: \(0.48 \times 1000 = 480.0\). This results in 480.
04

- Write the Final Answer

Confirm that the final answer to the multiplication problem is 480.

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Key Concepts

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

Multiplication by 1000
Multiplying a number by 1000 involves a simple yet powerful trick. When you do this, you essentially amplify the number by thousand times its original value. But how do you execute such a multiplication without complex arithmetic? It鈥檚 all about moving the decimal point. When you multiply any number by 1000, you shift the decimal point three places to the right. For instance, if you have the decimal number 0.48 and you need to multiply it by 1000, you will move the decimal point three slots to the right, resulting in 480.0. This makes 0.48 multiply to become 480, a considerably larger number. Shifting the decimal point is intuitive and super easy once you grasp the concept.
Moving Decimal Points
Understanding how to move decimal points is crucial in decimal multiplication. Moving the decimal point changes the value of the number, making it ten times larger with every place shifted to the right. Here鈥檚 a quick breakdown on how it works:
  • For instance, moving the decimal point one place to the right for 0.48 transforms it into 4.8.
  • Moving it two places shifts it to 48.
  • Three places makes it 480, as in our example of multiplying 0.48 by 1000.

Whenever you multiply by 10, 100, or 1000, you simply move the decimal point rightward by one, two, or three places, respectively. This technique dramatically simplifies the multiplication process, saving you from manual calculations.
Basic Arithmetic Operations
At the heart of solving any math problem lies understanding basic arithmetic operations. These operations include addition, subtraction, multiplication, and division. Multiplication, specifically, means finding the total number of objects in a number of identical groups. When you multiply decimals, it鈥檚 much the same as multiplying whole numbers, but you work a bit more with decimal points. Here鈥檚 how you approach it step by step:
  • First, align the numbers by their digits, ignoring the decimal points for now.
  • Then, multiply as if you were working with whole numbers.
  • Finally, move the decimal point back into the correct position in your final answer.
In our example, multiplying 0.48 by 1000 might seem daunting, but using decimal point shifts simplifies it. Basic arithmetic, when combined with these techniques, becomes an easier, faster way to solve problems.

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Most popular questions from this chapter

The United States earned 121 medals at the 2016 Summer Olympics. The number of silver medals earned was 1 fewer than the number of bronze medals. The number of gold medals earned was 8 more than the number of bronze medals. How many of each kind of medal did the United States earn? (Data from The World Almanac and Book of Facts.)

Find two consecutive odd integers such that twice the greater is 17 more than the lesser.

A workout that combines weight training and aerobics burns a total of 371 calories. If weight training burns \(\frac{2}{5}\) as many calories as aerobics, how many calories does weight training burn?

A three-foot-long deli sandwich must be split into three pieces so that the middle piece is twice as long as the shortest piece and the shortest piece is 8 in. shorter than the longest piece. How long should the three pieces be?

If five times the lesser of two consecutive integers is added to three times the greater, the result is \(59 .\) Find the integers.
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