Identifying the Place Value

Oct 13, 2025 by miodeya.com 11 views

When dividing numbers, understanding the place value of the last digit in the quotient is crucial for accurate calculations. In this article, we will explore the concept of place value in division and apply it to the given problem: dividing 8,164 by 78.5.

What is Place Value?

Place value refers to the value of a digit in a number based on its position. In the decimal system, each position represents a power of 10. The rightmost digit represents the ones place, the next digit to the left represents the tens place, and so on.

Understanding the Problem

The problem asks us to find the place value of the last digit in the quotient when dividing 8,164 by 78.5. To solve this problem, we need to perform the division and identify the place value of the last digit in the quotient.

Performing the Division

To divide 8,164 by 78.5, we can use long division or a calculator. Let's use long division to perform the calculation.

  ____________________
78.5 | 8,164
  - 78,000
  _______
      164
  - 156
  _______
        8
  - 0
  _______
        8

The quotient is 103.2.

Identifying the Place Value

Now that we have the quotient, we need to identify the place value of the last digit. The last digit in the quotient is 2. Since the quotient is a decimal number, we need to consider the decimal places.

Decimal Places

In the decimal system, each decimal place represents a power of 10. The rightmost decimal place represents the tenths place, the next decimal place to the left represents the hundredths place, and so on.

Applying the Concept

In the quotient 103.2, the last digit is 2, which is in the tenths place. Therefore, the place value of the last digit in the quotient is tenths.

Conclusion

In conclusion, when dividing 8,164 by 78.5, the place value of the last digit in the quotient is tenths. Understanding place value is essential for accurate calculations in division and other mathematical operations.

Common Mistakes

When performing division, it's common to make mistakes in identifying the place value of the last digit. To avoid these mistakes, make sure to:

Perform the division accurately
Identify the decimal places correctly
Consider the power of 10 for each decimal place

Real-World Applications

Understanding place value in division has real-world applications in various fields, such as:

Finance: When calculating interest rates or investment returns, accurate division is crucial.
Science: In scientific calculations, accurate division is essential for obtaining reliable results.
Engineering: In engineering calculations, accurate division is necessary for designing and building structures.

Practice Problems

To practice identifying the place value of the last digit in the quotient, try the following problems:

Divide 9,012 by 85.2 and identify the place value of the last digit.
Divide 6,480 by 92.1 and identify the place value of the last digit.
Divide 3,210 by 78.9 and identify the place value of the last digit.

Conclusion

Q: What is the place value of the last digit in the quotient when dividing 8,164 by 78.5? A: The place value of the last digit in the quotient is tenths.

Q: How do I identify the place value of the last digit in the quotient? A: To identify the place value of the last digit in the quotient, you need to perform the division accurately and consider the decimal places. The rightmost decimal place represents the tenths place, the next decimal place to the left represents the hundredths place, and so on.

Q: What is the difference between the ones place and the tenths place? A: The ones place represents the value of a digit in a number based on its position, while the tenths place represents the value of a digit in a decimal number based on its position.

Q: Can I use a calculator to perform division and identify the place value of the last digit? A: Yes, you can use a calculator to perform division and identify the place value of the last digit. However, make sure to understand the concept of place value and decimal places to ensure accurate calculations.

Q: How do I apply the concept of place value in real-world applications? A: In real-world applications, you can apply the concept of place value in division by considering the decimal places and the power of 10 for each decimal place. This is essential in fields such as finance, science, and engineering.

Q: What are some common mistakes to avoid when performing division and identifying the place value of the last digit? A: Some common mistakes to avoid when performing division and identifying the place value of the last digit include:

Not performing the division accurately
Not considering the decimal places correctly
Not understanding the concept of place value and decimal places

Q: Can I use the concept of place value in other mathematical operations, such as multiplication and addition? A: Yes, you can use the concept of place value in other mathematical operations, such as multiplication and addition. However, the concept of place value is more relevant in division and other operations that involve decimal numbers.

Q: How do I practice identifying the place value of the last digit in the quotient? A: You can practice identifying the place value of the last digit in the quotient by trying the following problems:

Divide 9,012 by 85.2 and identify the place value of the last digit.
Divide 6,480 by 92.1 and identify the place value of the last digit.
Divide 3,210 by 78.9 and identify the place value of the last digit.

Q: What are some real-world applications of the concept of place value in division? A: Some real-world applications of the concept of place value in division include:

Finance: When calculating interest rates or investment returns, accurate division is crucial.
Science: In scientific calculations, accurate division is essential for obtaining reliable results.
Engineering: In engineering calculations, accurate division is necessary for designing and building structures.

Q: Can I use the concept of place value in other fields, such as business or economics? A: Yes, you can use the concept of place value in other fields, such as business or economics. However, the concept of place value is more relevant in fields that involve mathematical calculations and decimal numbers.

Conclusion

In conclusion, understanding the concept of place value in division is essential for accurate calculations. By applying the concept of place value, you can identify the place value of the last digit in the quotient and perform calculations with confidence.