Understanding Place Value in Numbers

Oct 13, 2025 by pinkandtrash.com 60 views

Understanding Place Value in Numbers

Place value is a fundamental concept in mathematics that helps us understand the value of each digit in a number. It is the value that a digit holds in a number based on its position. In the decimal system, each position in a number has a specific place value, which is determined by the power of 10. The place value of a digit increases as we move from left to right in a number.

Identifying the 6-digit in the Number 205.876

To determine the place value of the 6-digit in the number 205.876, we need to identify the digit and its position in the number. The number 205.876 has six digits: 2, 0, 5, 8, 7, and 6. The digit 6 is the 6-digit in the number.

Understanding the Decimal System

The decimal system is a base-10 number system, which means that each position in a number has a place value that is a power of 10. The place values in the decimal system are as follows:

Ones (1)
Tens (10)
Hundreds (100)
Thousands (1000)
Ten thousands (10,000)
Hundred thousands (100,000)
Millions (1,000,000)
Ten millions (10,000,000)
Hundred millions (100,000,000)
Billions (1,000,000,000)
And so on.

Determining the Place Value of the 6-digit

Since the number 205.876 is a decimal number, we need to consider the decimal point when determining the place value of the 6-digit. The decimal point separates the whole number part from the fractional part. The whole number part is 205, and the fractional part is 0.876.

The 6-digit is the last digit in the fractional part, which is 6. To determine the place value of the 6-digit, we need to consider the position of the decimal point. The decimal point is between the 5 and the 8. This means that the 6-digit is in the thousandths place.

Conclusion

The place value of the 6-digit in the number 205.876 is thousandths. This is because the 6-digit is the last digit in the fractional part, and the decimal point is between the 5 and the 8.

Answer

The correct answer is D. Thousandths.

Frequently Asked Questions

Q: What is the place value of the 6-digit in the number 205.876?

A: The place value of the 6-digit in the number 205.876 is thousandths.

Q: Why is the 6-digit in the thousandths place?

A: The 6-digit is in the thousandths place because it is the last digit in the fractional part, and the decimal point is between the 5 and the 8.

Q: What is the decimal system?

A: The decimal system is a base-10 number system, which means that each position in a number has a place value that is a power of 10.

Q: What are the place values in the decimal system?

A: The place values in the decimal system are ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, ten millions, hundred millions, billions, and so on.

Example Problems

Problem 1

What is the place value of the 7-digit in the number 432.198?

A: The place value of the 7-digit in the number 432.198 is ten-thousandths.

Problem 2

What is the place value of the 5-digit in the number 987.654?

A: The place value of the 5-digit in the number 987.654 is ten-thousandths.

Problem 3

What is the place value of the 3-digit in the number 123.456?

A: The place value of the 3-digit in the number 123.456 is ten-thousandths.

Practice Problems

Problem 1

What is the place value of the 9-digit in the number 987.654.321?

A: _____________________________________

Problem 2

What is the place value of the 2-digit in the number 12.345?

A: _____________________________________

Problem 3

What is the place value of the 8-digit in the number 876.543.21?

A: _____________________________________

Summary

In this article, we learned about the place value of the 6-digit in the number 205.876. We understood the concept of place value and how it is determined in the decimal system. We identified the 6-digit in the number and determined its place value as thousandths. We also answered frequently asked questions and provided example problems and practice problems to help reinforce the concept.

Understanding Place Value

Q&A

Q: What is the place value of the 6-digit in the number 205.876?

A: The place value of the 6-digit in the number 205.876 is thousandths.

Q: Why is the 6-digit in the thousandths place?

A: The 6-digit is in the thousandths place because it is the last digit in the fractional part, and the decimal point is between the 5 and the 8.

Q: What is the decimal system?

A: The decimal system is a base-10 number system, which means that each position in a number has a place value that is a power of 10.

Q: What are the place values in the decimal system?

A: The place values in the decimal system are ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, ten millions, hundred millions, billions, and so on.

Q: How do I determine the place value of a digit in a number?

A: To determine the place value of a digit in a number, you need to identify the position of the digit and the power of 10 that corresponds to that position.

Q: What is the difference between the place value and the face value of a digit?

A: The face value of a digit is the value of the digit itself, while the place value is the value of the digit based on its position in the number.

Q: Can you give an example of how to determine the place value of a digit in a number?

A: Yes, let's consider the number 432.198. The digit 8 is in the thousandths place because it is the last digit in the fractional part, and the decimal point is between the 5 and the 8.

Q: How do I convert a number from one place value to another?

A: To convert a number from one place value to another, you need to multiply or divide the number by the corresponding power of 10.

Q: What is the importance of understanding place value in mathematics?

A: Understanding place value is essential in mathematics because it helps us perform calculations, solve problems, and understand the relationships between numbers.

Q: Can you give an example of how understanding place value can help us solve a problem?

A: Yes, let's consider the problem of finding the sum of two numbers: 432.198 and 987.654. To solve this problem, we need to understand the place value of each digit in the numbers and perform the calculation accordingly.

Q: How do I practice understanding place value?

A: You can practice understanding place value by working on problems that involve identifying the place value of digits in numbers, converting numbers from one place value to another, and performing calculations that involve place value.

Example Problems

Problem 1

What is the place value of the 7-digit in the number 987.654.321?

A: The place value of the 7-digit in the number 987.654.321 is ten-thousandths.

Problem 2

What is the place value of the 5-digit in the number 123.456.789?

A: The place value of the 5-digit in the number 123.456.789 is ten-thousandths.

Problem 3

What is the place value of the 3-digit in the number 987.654.321?

A: The place value of the 3-digit in the number 987.654.321 is ten-thousandths.

Practice Problems

Problem 1

What is the place value of the 9-digit in the number 987.654.321.987?

A: _____________________________________

Problem 2

What is the place value of the 2-digit in the number 12.345.678?

A: _____________________________________

Problem 3

What is the place value of the 8-digit in the number 876.543.210.987?

A: _____________________________________

Summary

In this article, we answered frequently asked questions about place value and provided example problems and practice problems to help reinforce the concept. We also discussed the importance of understanding place value in mathematics and how it can help us solve problems.