002. Place Value and Comparing Numbers

Learning Intentions

• To understand how place value works in the Hindu–Arabic (decimal) number system
• identify the place value of digits in different numbers
• convert between basic numerals and their expanded form
• compare two positive integers by considering the digits and their place value

Pre-requisite Summary

• Understanding that digits 0–9 are used to form numbers
• Knowing that each place is ten times the value of the place to its right
• Reading whole numbers correctly
• Understanding ones, tens, hundreds, and thousands
• Recognising that the position of a digit changes its value
• Familiarity with addition of place values
• Understanding inequality symbols (<, >, =)
• Comparing numbers by magnitude

Worked Examples

Worked Example 1

Explain how place value works in the number 4,582.
a) Identify the value of each digit
b) Explain why the 5 represents 500 and not 5

Worked Example 2

Identify the place value of the bolded digit.
a) 6,341
b) 82,509

Worked Example 3

Write the following numbers in expanded form.
a) 3,406
b) 72,915

Worked Example 4

Write the expanded form as a single number.
a) 5,000 + 300 + 40 + 2
b) 70,000 + 8,000 + 6 + 1

Worked Example 5

Compare the numbers using <, > or =
a) 4,562 ___ 4,526
b) 19,305 ___ 9,850

Worked Example 6

Compare the numbers by place value.
a) 72,018 and 72,180
b) 5,904 and 5,940

Problems

Problem 1

Explain how place value works in the number 7,364.
a) Identify the value of each digit
b) Explain why the 3 represents 300

Problem 2

Identify the place value of the bolded digit.
a) 5,782
b) 43,916

Problem 3

Write the following numbers in expanded form.
a) 6,205
b) 81,430

Problem 4

Write the expanded form as a single number.
a) 9,000 + 400 + 60 + 8
b) 20,000 + 3,000 + 90 + 5

Problem 5

Compare the numbers using <, > or =
a) 8,451 ___ 8,415
b) 27,304 ___ 27,430

Problem 6

Compare the numbers by place value.
a) 64,109 and 64,190
b) 3,875 and 3,785

Exercises

Understanding and Fluency

1. Identify the value of each digit in 5,284
2. Identify the value of each digit in 90,613
3. Write 4,705 in expanded form
4. Write 63,209 in expanded form
5. Write 8,000 + 200 + 30 + 9 as a number
6. Write 50,000 + 4,000 + 600 + 2 as a number
7. Compare: 6,215 ___ 6,251
8. Compare: 14,802 ___ 14,820
9. Compare: 39,105 ___ 40,001
10. Compare: 7,450 ___ 7,405

Reasoning

11. A student says 3,405 is the same as 3,45. Explain the error.
12. Why does the number 5,000 have fewer digits than 4,999 but is larger?
13. Explain why 6,109 is greater than 6,091.
14. Two numbers both have 5 in the thousands place. What must you check next to compare them?

Problem-solving

15. Create a 4-digit number with a 7 in the hundreds place and write it in expanded form.
16. Write two numbers that differ only in the tens place and compare them.
17. A number has digits 4, 8, 2, and 1. Make the largest possible number and write it in expanded form.
18. Write a number between 6,500 and 6,600 and explain how you know.

Potential Misunderstandings

• Students may think a digit always has the same value regardless of position.
• Students may confuse place value with face value.
• Students may omit zero placeholders in expanded form.
• Students may compare numbers based on the last digit only.
• Students may incorrectly align digits when comparing numbers.
• Students may think more digits always means a smaller number.

Next: 003. Mental Strategies and Laws for Addition and Subtraction