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Chapter 2: Problem 24

Multiply as indicated. 24\. \(0.84 \times 1000\)

Short Answer

Expert verified
840

Step by step solution

01

Understand the Multiplication

The problem is to multiply the decimal number 0.84 by 1000. Multiplying by 1000 is the same as moving the decimal point three places to the right.
02

Move the Decimal Point

Take the number 0.84. To multiply by 1000, move the decimal point three places to the right. Starting from 0.84, we move the decimal one place to get 8.4, two places to get 84, and a third place to get 840.
03

Write the Result

After moving the decimal three places to the right, the resulting number is 840.

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Key Concepts

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

moving decimal points
To multiply or divide decimals by factors of 10, we rely on the movement of decimal points rather than performing what might at first appear to be complex arithmetic. When we multiply a number by 10, 100, 1000, and so on, we move the decimal point to the right. The number of places we move the decimal point corresponds to the number of zeros in the factor. For example:
  • Multiplying by 10 means moving the decimal point one place to the right.
  • Multiplying by 100 involves moving the decimal two places to the right.
  • Multiplying by 1000 requires moving the decimal three places to the right.
In contrast, dividing by these same factors moves the decimal point to the left. This technique is straightforward once understood, reducing potential errors and simplifying computations.
multiplication by 1000
When we multiply a decimal number by 1000, we're effectively scaling up the number by three places. Imagine a decimal number like 0.84. Keeping in mind the rules of moving decimals:
  • Move the decimal one place to the right to get 8.4.
  • Move the decimal a second place to get 84.
  • Finally, move the decimal a third place to achieve 840.
Thus, multiplying 0.84 by 1000 gives us 840. This concept is powerful because it visualizes decimal multiplication as a simple, systematic process rather than treating it as a conventional large number multiplication.
decimal numbers
Decimal numbers are an extension of the base-10 number system we use daily, representing fractions and whole values simultaneously. Decimals are formed by placing digits to the right of a decimal point, which signifies values less than one. For example, 0.5 represents a half, while 0.84 is equivalent to 84 hundredths.

When working with decimals in multiplication:
  • Always align the decimal points to prevent errors.
  • Use the moving decimal technique for simpler calculations involving factors of 10, 100, or 1000.
This aligns numerical insights closely with real-world measurements, such as currency, length, and weight, making decimals a critical mathematical element.

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Most popular questions from this chapter

A one-cup serving of orange juice contains \(3 \mathrm{mg}\) less than four times the amount of vitamin \(\mathrm{C}\) as a one-cup serving of pineapple juice. Servings of the two juices contain a total of \(122 \mathrm{mg}\) of vitamin \(\mathrm{C}\). How many milligrams of vitamin \(\mathrm{C}\) are in a serving of each type of juice? (Data from U.S. Agriculture Department.)

Solve each formula for the specified variable. \(A x+B y=C\) for \(y\)

During the 115 th session, the total number of Democrats and Republicans in the U.S. House of Representatives was \(434 .\) There were 46 more Republicans than Democrats. How many members of each party were there? (Data from www.house.gov)

If 3 is added to a number and this sum is doubled, the result is 2 more than the number. Find the number.

Solve each equation for \(y\) $$ 3 x+y=6 $$
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