Reading and writing 4–5 digit numbers (Up to 100000).

Reading & Writing 4-5 Digit Numbers (up to 100,000)

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Lesson Objectives

  • Understand the place value of ten-thousands, thousands, hundreds, tens, and ones in 4-5 digit numbers.
  • Read and write 4-5 digit numbers in words and digits.
  • Express 4-5 digit numbers in expanded form (e.g., 34,567 = 30,000 + 4,000 + 500 + 60 + 7).
  • Compare and order 4-5 digit numbers up to 100,000 using symbols (>, <, =).
  • Apply place value knowledge to solve problems involving larger numbers.

Introduction to 4-5 Digit Numbers

A 4-digit number has four digits: thousands, hundreds, tens, and ones. A 5-digit number has five digits: ten-thousands, thousands, hundreds, tens, and ones. The largest 4-digit number is 9,999, and the largest 5-digit number is 99,999. Understanding these larger numbers helps us count big groups, measure distances, and work with money in the thousands.

Key Concepts for This Lesson
• A 4-digit number has a thousands, hundreds, tens, and ones place.
• A 5-digit number has a ten-thousands, thousands, hundreds, tens, and ones place.
• Example: 34,567 has 3 ten-thousands, 4 thousands, 5 hundreds, 6 tens, and 7 ones.
• Expanded form: 34,567 = 30,000 + 4,000 + 500 + 60 + 7.
• Word form: 34,567 = "thirty-four thousand five hundred sixty-seven".
• The number 100,000 is the smallest 6-digit number (1 hundred-thousand).
Key Definitions:
• Digit: A single number symbol (0–9).
• Place Value: The value of a digit based on its position in the number.
• Ten-Thousands: The fifth digit from the right (e.g., in 34,567, the 3 is in the ten-thousands place).
• Thousands: The fourth digit from the right (e.g., in 34,567, the 4 is in the thousands place).
• Commas: Used in numbers to separate thousands (e.g., 34,567).

Quick Reference: Place Value Chart

NumberTen-ThousandsThousandsHundredsTensOnesExpanded Form
45,6784567840,000 + 5,000 + 600 + 70 + 8
9,045090450 + 9,000 + 0 + 40 + 5
70,2037020370,000 + 0 + 200 + 0 + 3
99,9999999990,000 + 9,000 + 900 + 90 + 9

Scroll sideways on smaller screens to view the full table.

Place Value (Ten-Thousands, Thousands, Hundreds, Tens, Ones)

Every 4-5 digit number has places for ten-thousands, thousands, hundreds, tens, and ones. The ten-thousands place tells how many groups of 10,000, the thousands place tells how many groups of 1,000, the hundreds place tells how many groups of 100, the tens place tells how many groups of 10, and the ones place tells how many individual units.

Step-by-Step: Finding Place Value
1. Write the number and identify each digit from right to left.
2. The first digit (rightmost) is the ones place.
3. The second digit is the tens place.
4. The third digit is the hundreds place.
5. The fourth digit is the thousands place.
6. The fifth digit is the ten-thousands place.
7. Multiply each digit by its place value and add them to get the number.
Place Value of 5-Digit Numbers 3 Ten-Thousands 4 Thousands 5 Hundreds 6 Tens 7 Ones 34,567 = 30,000 + 4,000 + 500 + 60 + 7

The number 34,567 has 3 ten-thousands, 4 thousands, 5 hundreds, 6 tens, and 7 ones. It is the sum of 30,000, 4,000, 500, 60, and 7.

Example 1: Identifying Place Value
Problem: What is the value of the digit 7 in the number 47,892?

Solution:
Step 1: Write the number: 47,892.

Step 2: The digits are 4, 7, 8, 9, and 2. The 7 is in the thousands place (fourth from the right).

Step 3: The value of 7 in the thousands place is 7 × 1,000 = 7,000.

Answer: The value of 7 is 7,000.
Example 2: Building a Number
Problem: What number has 5 ten-thousands, 2 thousands, 8 hundreds, 3 tens, and 6 ones?

Solution:
Step 1: Write the ten-thousands digit: 5.

Step 2: Write the thousands digit: 2.

Step 3: Write the hundreds digit: 8.

Step 4: Write the tens digit: 3.

Step 5: Write the ones digit: 6.

Step 6: Combine: 52,836.

Answer: The number is 52,836.
Watch Out!
Remember that the value of a digit depends on its position. The digit 3 in 35,678 has a value of 30,000, while in 53,678 it has a value of 3,000.

Practice for Place Value

  1. What is the value of the digit 6 in 61,392?
  2. What number has 8 ten-thousands, 0 thousands, 4 hundreds, 2 tens, and 5 ones?
  3. In the number 90,415, what digit is in the hundreds place?
  4. What is the value of the digit 9 in 29,870?
  5. Write the number with 4 ten-thousands, 3 thousands, 0 hundreds, 7 tens, and 8 ones.

Reading Numbers in Words

To read a 4-5 digit number in words, say the ten-thousands and thousands as one number, then "thousand", then the remaining three-digit number (hundreds, tens, ones). If the thousands part is zero, just say the ten-thousands part as "thousand".

Step-by-Step: Reading a 4-5 Digit Number
1. Read the digits before the comma as one number and say "thousand".
2. Read the remaining three digits as a 3-digit number.
3. For numbers like 45,000, say "forty-five thousand".
4. For numbers like 60,000, say "sixty thousand".
5. Use hyphens between tens and ones (e.g., "sixty-seven").
Example 3: Reading Numbers in Words
Problem: Write the following numbers in words: 48,273; 60,500; 99,004.

Solution:
Step 1: 48,273 = forty-eight thousand two hundred seventy-three.

Step 2: 60,500 = sixty thousand five hundred.

Step 3: 99,004 = ninety-nine thousand four.

Answer: 48,273 = forty-eight thousand two hundred seventy-three; 60,500 = sixty thousand five hundred; 99,004 = ninety-nine thousand four.
Example 4: Writing Numbers from Words
Problem: Write the following as numbers: seventy-two thousand three hundred forty-five, eighty thousand two, fifty-six thousand seven hundred.

Solution:
Step 1: seventy-two thousand three hundred forty-five = 72,345.

Step 2: eighty thousand two = 80,002.

Step 3: fifty-six thousand seven hundred = 56,700.

Answer: 72,345, 80,002, 56,700.
Watch Out!
When reading numbers with zeros, be careful not to say "and" (e.g., 80,002 is "eighty thousand two", not "eighty thousand and two").

Practice for Reading Numbers in Words

  1. Write 62,189 in words.
  2. Write 90,040 in words.
  3. Write 71,005 in words.
  4. Write "thirty-five thousand eight hundred twenty-one" as a number.
  5. Write "forty-three thousand five" as a number.

Writing Numbers in Expanded Form

Expanded form shows the value of each digit in a number. For a 4-5 digit number, it is the sum of the ten-thousands, thousands, hundreds, tens, and ones values.

Step-by-Step: Writing in Expanded Form
1. Identify the ten-thousands digit and multiply it by 10,000.
2. Identify the thousands digit and multiply it by 1,000.
3. Identify the hundreds digit and multiply it by 100.
4. Identify the tens digit and multiply it by 10.
5. Identify the ones digit.
6. Write the sum of these five values.
Example 5: Expanded Form (5-Digit)
Problem: Write 83,672 in expanded form.

Solution:
Step 1: Ten-thousands digit is 8 → 8 × 10,000 = 80,000.

Step 2: Thousands digit is 3 → 3 × 1,000 = 3,000.

Step 3: Hundreds digit is 6 → 6 × 100 = 600.

Step 4: Tens digit is 7 → 7 × 10 = 70.

Step 5: Ones digit is 2 → 2.

Step 6: Sum: 80,000 + 3,000 + 600 + 70 + 2.

Answer: 83,672 = 80,000 + 3,000 + 600 + 70 + 2.
Example 6: Expanded Form (4-Digit)
Problem: Write 9,045 in expanded form.

Solution:
Step 1: Thousands digit is 9 → 9 × 1,000 = 9,000.

Step 2: Hundreds digit is 0 → 0 × 100 = 0.

Step 3: Tens digit is 4 → 4 × 10 = 40.

Step 4: Ones digit is 5 → 5.

Step 5: Sum: 9,000 + 0 + 40 + 5.

Answer: 9,045 = 9,000 + 0 + 40 + 5.
Watch Out!
Make sure to include zeros in expanded form if a digit is zero. For example, 40,502 = 40,000 + 0 + 500 + 0 + 2.

Practice for Expanded Form

  1. Write 56,238 in expanded form.
  2. Write 70,406 in expanded form.
  3. Write 9,100 in expanded form.
  4. What number is 40,000 + 3,000 + 200 + 50 + 6?
  5. What number is 80,000 + 0 + 700 + 0 + 3?

Comparing & Ordering Numbers

To compare 4-5 digit numbers, compare the ten-thousands digits first. If they are equal, compare the thousands digits, then hundreds, tens, and ones. Use symbols: > (greater than), < (less than), = (equal to).

Step-by-Step: Comparing Numbers
1. Compare the ten-thousands digits. The larger digit means the number is larger.
2. If the ten-thousands digits are equal, compare the thousands digits.
3. If the thousands digits are also equal, compare the hundreds digits.
4. Continue with tens, then ones.
5. Use <, >, or = to show the relationship.
Example 7: Comparing Numbers
Problem: Compare 45,678 and 45,789.

Solution:
Step 1: Both have 4 in the ten-thousands place.

Step 2: Both have 5 in the thousands place.

Step 3: Compare hundreds: 6 vs 7. 6 is less than 7, so 45,678 < 45,789.

Answer: 45,678 < 45,789.
Example 8: Ordering Numbers
Problem: Order these numbers from least to greatest: 38,976; 39,012; 38,750; 39,100.

Solution:
Step 1: Compare ten-thousands: all have 3.

Step 2: Compare thousands: 38,xxx vs 39,xxx. So 38,xxx < 39,xxx.

Step 3: For 38,xxx: compare hundreds: 976 vs 750. 38,750 < 38,976.

Step 4: For 39,xxx: compare hundreds: 012 vs 100. 39,012 < 39,100.

Step 5: Order: 38,750; 38,976; 39,012; 39,100.

Answer: 38,750; 38,976; 39,012; 39,100.
Watch Out!
When comparing numbers, always start with the highest place value (ten-thousands). Do not compare ones digits first!

Practice for Comparing & Ordering

  1. Compare: 61,234 ☐ 61,243 (use >, <, or =)
  2. Compare: 80,070 ☐ 80,700
  3. Compare: 99,999 ☐ 99,998
  4. Order these from greatest to least: 45,000; 45,500; 44,999; 45,001.
  5. Order these from least to greatest: 12,345; 12,543; 12,354; 12,435.

Cumulative Practice Exercises

  1. What is the value of the digit 9 in 93,278?
  2. Write 74,206 in words.
  3. Write 80,030 in expanded form.
  4. Compare: 65,432 ☐ 65,423 (use >, <, or =)
  5. Order these numbers from least to greatest: 23,456; 23,546; 23,465; 23,654.
  6. What number is 60,000 + 4,000 + 300 + 20 + 8?
  7. Write "eighty-nine thousand five hundred seventy-one" as a number.
  8. What is the value of the digit 4 in 74,682?
  9. Write 90,017 in expanded form.
  10. Compare: 83,001 ☐ 83,010 (use >, <, or =)
  11. Order these from greatest to least: 55,555; 55,505; 55,550; 55,500.
  12. What number has 7 ten-thousands, 2 thousands, 8 hundreds, 0 tens, and 4 ones?
  13. Write 12,034 in words.
  14. What is the value of the digit 6 in 16,789?
  15. Compare: 99,999 ☐ 100,000 (use >, <, or =)
Show/Hide Answers

Solutions to Cumulative Exercises

  1. Step 1: In 93,278, the 9 is in the ten-thousands place.
    Answer: 90,000.
  2. Step 1: 74,206 = seventy-four thousand two hundred six.
    Answer: seventy-four thousand two hundred six.
  3. Step 1: 80,030 = 80,000 + 0 + 0 + 30 + 0.
    Answer: 80,000 + 0 + 0 + 30 + 0.
  4. Step 1: 65,432 vs 65,423: ten-thousands same (6), thousands same (5), hundreds same (4), tens: 3 vs 2. 65,432 > 65,423.
    Answer: 65,432 > 65,423.
  5. Step 1: All in the 23,000s. Order: 23,456; 23,465; 23,546; 23,654.
    Answer: 23,456; 23,465; 23,546; 23,654.
  6. Step 1: 60,000 + 4,000 + 300 + 20 + 8 = 64,328.
    Answer: 64,328.
  7. Step 1: eighty-nine thousand = 89,000; five hundred seventy-one = 571.
    Answer: 89,571.
  8. Step 1: In 74,682, the 4 is in the thousands place.
    Answer: 4,000.
  9. Step 1: 90,017 = 90,000 + 0 + 0 + 10 + 7.
    Answer: 90,000 + 0 + 0 + 10 + 7.
  10. Step 1: 83,001 vs 83,010: ten-thousands same (8), thousands same (3), hundreds same (0), tens: 0 vs 1. 83,001 < 83,010.
    Answer: 83,001 < 83,010.
  11. Step 1: All in the 55,000s. Order: 55,555; 55,550; 55,505; 55,500.
    Answer: 55,555; 55,550; 55,505; 55,500.
  12. Step 1: 7 ten-thousands = 70,000; 2 thousands = 2,000; 8 hundreds = 800; 0 tens = 0; 4 ones = 4.
    Answer: 72,804.
  13. Step 1: 12,034 = twelve thousand thirty-four.
    Answer: twelve thousand thirty-four.
  14. Step 1: In 16,789, the 6 is in the thousands place.
    Answer: 6,000.
  15. Step 1: 99,999 vs 100,000: compare ten-thousands: 9 vs 10. 99,999 < 100,000.
    Answer: 99,999 < 100,000.

Conclusion & Summary

Reading and writing 4-5 digit numbers is an essential skill for everyday math. By understanding place value up to the ten-thousands, you can read any number up to 99,999, write it in expanded form, and compare numbers. These skills will help you with addition, subtraction, and more advanced math topics involving large numbers.

Key Takeaways:
1. Place Value: 4-5 digit numbers have ten-thousands, thousands, hundreds, tens, and ones places.
2. Reading: Say the ten-thousands and thousands, then "thousand", then the remaining three digits.
3. Expanded Form: 34,567 = 30,000 + 4,000 + 500 + 60 + 7.
4. Comparing: Compare ten-thousands first, then thousands, then hundreds, tens, and ones.
5. Ordering: Arrange numbers from least to greatest or greatest to least.

Keep practicing with large numbers—you'll see them in population counts, distances, and money!

Video Resource

Watch this video for more examples of reading and writing large numbers.

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