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Chapter 8: Problem 48

Divide. $$ 23.4 \div 1000 $$

Short Answer

Expert verified
0.0234

Step by step solution

01

Understand Division by 1000

When dividing a number by 1000, you need to move the decimal point three places to the left. This is because 1000 has three zeros.
02

Identify the Current Position of the Decimal Point

The current position of the decimal point in the number 23.4 is between the digits 3 and 4.
03

Move the Decimal Point Three Places to the Left

Move the decimal point in 23.4 three places to the left: 23.4 鈫� 2.34 鈫� 0.234 鈫� 0.0234. Now, the decimal point is placed before the digits.
04

Verify the New Number

Check the new value obtained after moving the decimal point, which is 0.0234. Ensure that it is correctly calculated by verifying the steps.

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Key Concepts

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

decimal point
When working with decimal points, understanding their position in a number is crucial. The decimal point separates the whole number part from the fractional part. In the number 23.4, the decimal point is between the digits 3 and 4. This helps us understand the value of each digit based on its position relative to the decimal point. For instance, in 23.4, the digit 2 stands for 20, the digit 3 stands for 3, and the digit 4 stands for 0.4. Moving the decimal point left or right can significantly change the number's value, which is particularly important in operations like division.
division steps
Dividing by a number, especially a power of 10 like 1000, follows a simple step-by-step process. To divide by 1000, move the decimal point three places to the left. This is because 1000 has three zeros:
  • First, identify the current position of the decimal point. It's at 23.4.
  • Move the decimal point one place to the left to get 2.34.
  • Move it another place left to get 0.234.
  • Finally, move it one more place to the left to get 0.0234.
Each step must be carefully verified to ensure the decimal point placement is correct, resulting in the accurate new value of 0.0234 when dividing by 1000.
mathematics operations
Mathematical operations like division involving decimal points can sometimes be tricky. Division, particularly like in our problem 23.4 梅 1000, highlights the importance of understanding both movement of decimal points and the division process itself. Simple rules such as moving the decimal point to the left for division by powers of 10 are very useful.
These operations can have applications in various real-world scenarios, such as converting units or working in scientific calculations. Engaging with such problems enhances numerical understanding and problem-solving skills, vital components in mathematics education.

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