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Chapter 2: Problem 17

Multiply as indicated. 17\. \(0.1 \times 100\)

Short Answer

Expert verified
10

Step by step solution

01

- Understand the Problem

The exercise asks to multiply two numbers: 0.1 and 100.
02

- Setting Up the Multiplication

Write the multiplication expression: \[ 0.1 \times 100 \]
03

- Calculate the Multiplication

Perform the multiplication by moving the decimal point two places to the right. Hence, \[0.1 \times 100 = 10\]
04

- Verify the Result

Confirm the calculation by recognizing that multiplying by 100 moves the decimal point two places to the right.

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Key Concepts

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

decimal multiplication
When dealing with multiplication involving decimals, it鈥檚 important to understand how to handle the decimal points. Multiplying decimals follows the same principles as multiplying whole numbers, and then you adjust for the decimal point at the end.

Imagine you are multiplying 0.1 and 100. The process involves simple multiplication, but you need to adjust the placement of the decimal point in the final product to get the correct result. Let鈥檚 break it down further.
moving decimal points
One of the key steps in multiplying decimals is correctly placing the decimal point in the product. Here鈥檚 how you can do it:
  • First, multiply the numbers as if they were whole numbers.

  • Next, count the total number of decimal places in both of the numbers you are multiplying.

  • Finally, place the decimal in the product so that it contains the same number of decimal places counted in the previous step.
For instance, in 0.1 脳 100, we first ignore the decimal and calculate 1 脳 100 = 100.
Next, count the decimal places: 0.1 has 1 decimal place and 100 has 0, which sums up to 1 decimal place.
Therefore, place the decimal point in 100 to get: 10.0, which simplifies to 10.
steps to multiply numbers
To ensure you understand how to multiply decimals properly, follow these steps:
  • Understand the Problem: Identify the numbers to be multiplied, noting their decimal places.

  • Setting Up the Multiplication: Write the expression, ignoring the decimals initially. This step simplifies the multiplication process.

  • Calculate the Multiplication: Multiply the numbers as if they were whole numbers. For example, for 0.1 脳 100, think of it as 1 脳 100 first, which equals 100.

  • Adjust for Decimals: Count the total number of decimal places in the original numbers. Move the decimal point in the product accordingly to reflect the correct number of decimal places.

  • Verify the Result: Check your result by ensuring the placement of the decimal point makes sense given the multiplication operation.
Following these steps will help you accurately perform decimal multiplication every time.

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