/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 37 $$ \frac{213.4567}{1000} $$... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 37

$$ \frac{213.4567}{1000} $$

Short Answer

Expert verified
0.2134567

Step by step solution

01

Understand the Division

The exercise asks to divide 213.4567 by 1000. Dividing by 1000 simply involves moving the decimal point.
02

Move the Decimal Point

To divide by 1000, move the decimal point three places to the left. Start with the number 213.4567.
03

Apply the Decimal Shift

Moving the decimal point three places to the left changes 213.4567 to 0.2134567.

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Key Concepts

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

Dividing by Powers of 10
Dividing by powers of 10, like 10, 100, or 1000, is a fundamental skill in arithmetic. When dividing a number by a power of 10, you don't necessarily need a calculator. It's all about understanding how many places you need to move the decimal point.
Powers of 10 are numbers like 10, 100, 1000, etc., where each subsequent number is 10 times larger than the previous one.
For instance:
  • When dividing by 10, you move the decimal point one place to the left.
  • When dividing by 100, you move the decimal point two places to the left.
  • When dividing by 1000, you move the decimal point three places to the left.
Let's look at our specific example of dividing 213.4567 by 1000. We will soon learn how to shift the decimal point accordingly.
Decimal Point Movement
The concept of decimal point movement is crucial when dealing with powers of 10. As explained, dividing by a power of 10 simplifies to shifting the decimal point. In our case with \(\frac{213.4567}{1000}\), here's how the process works:
  • Start with the number 213.4567.
  • Because we are dividing by 1000, move the decimal point three spaces to the left.
Visualize it as:
  • 213.4567 (original number)
  • 21.34567
  • 2.134567
  • 0.2134567 (final result after moving three spaces)

By shifting the decimal point three places to the left, we obtain 0.2134567. Hence, \(\frac{213.4567}{1000}\) equals 0.2134567.
Always remember, moving the decimal to the left makes the number smaller.
Basic Arithmetic Skills
Mastering basic arithmetic skills builds the foundation for more complex math problems. These skills include understanding operations like addition, subtraction, multiplication, and division.
For division, particularly, one key aspect is understanding when to use decimal points and how to manipulate them.
In our example of dividing 213.4567 by 1000, knowing how to move the decimal point is an essential skill. Rely on these fundamentals to solve many practical math problems without the need for advanced tools. Use these tips as a quick reference:
  • Practice moving decimal points in different scenarios.
  • Understand the significance of each power of 10.
  • Work on simple division exercises to strengthen your basic arithmetic skills.

With consistent practice and understanding these core concepts, you'll find arithmetic operations much simpler and logical.

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Most popular questions from this chapter

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