Reading and writing 5–6 digit numbers.

Reading & Writing 5-6 Digit Numbers (up to 1,000,000)

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Lesson Objectives

  • Understand the place value of hundred-thousands, ten-thousands, thousands, hundreds, tens, and ones in 5-6 digit numbers.
  • Read and write 5-6 digit numbers in words and digits.
  • Express 5-6 digit numbers in expanded form (e.g., 345,678 = 300,000 + 40,000 + 5,000 + 600 + 70 + 8).
  • Compare and order 5-6 digit numbers up to 1,000,000 using symbols (>, <, =).
  • Apply place value knowledge to solve problems involving large numbers.

Introduction to 5-6 Digit Numbers

A 5-digit number has five digits: ten-thousands, thousands, hundreds, tens, and ones. A 6-digit number has six digits: hundred-thousands, ten-thousands, thousands, hundreds, tens, and ones. The largest 5-digit number is 99,999, and the largest 6-digit number is 999,999. Understanding these larger numbers helps us count populations, distances, and large amounts of money.

Key Concepts for This Lesson
• A 5-digit number has ten-thousands, thousands, hundreds, tens, and ones places.
• A 6-digit number has hundred-thousands, ten-thousands, thousands, hundreds, tens, and ones places.
• Example: 345,678 has 3 hundred-thousands, 4 ten-thousands, 5 thousands, 6 hundreds, 7 tens, and 8 ones.
• Expanded form: 345,678 = 300,000 + 40,000 + 5,000 + 600 + 70 + 8.
• Word form: 345,678 = "three hundred forty-five thousand six hundred seventy-eight".
• The number 1,000,000 is the smallest 7-digit number (1 million).
Key Definitions:
• Digit: A single number symbol (0–9).
• Place Value: The value of a digit based on its position in the number.
• Hundred-Thousands: The sixth digit from the right (e.g., in 345,678, the 3 is in the hundred-thousands place).
• Ten-Thousands: The fifth digit from the right (e.g., in 345,678, the 4 is in the ten-thousands place).
• Thousands: The fourth digit from the right (e.g., in 345,678, the 5 is in the thousands place).
• Commas: Used in numbers to separate thousands (e.g., 345,678).

Quick Reference: Place Value Chart

NumberHundred-ThousandsTen-ThousandsThousandsHundredsTensOnesExpanded Form
345,678345678300,000 + 40,000 + 5,000 + 600 + 70 + 8
90,4050904050 + 90,000 + 0 + 400 + 0 + 5
700,203700203700,000 + 0 + 0 + 200 + 0 + 3
999,999999999900,000 + 90,000 + 9,000 + 900 + 90 + 9

Scroll sideways on smaller screens to view the full table.

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

Every 5-6 digit number has places for hundred-thousands, ten-thousands, thousands, hundreds, tens, and ones. The hundred-thousands place tells how many groups of 100,000, 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. The sixth digit is the hundred-thousands place.
8. Multiply each digit by its place value and add them to get the number.
Place Value of 6-Digit Numbers 3 Hundred-
Thousands 4 Ten-
Thousands 5 Thousands 6 Hundreds 7 Tens 8 Ones 345,678 = 300,000 + 40,000 + 5,000 + 600 + 70 + 8

The number 345,678 has 3 hundred-thousands, 4 ten-thousands, 5 thousands, 6 hundreds, 7 tens, and 8 ones. It is the sum of 300,000, 40,000, 5,000, 600, 70, and 8.

Example 1: Identifying Place Value
Problem: What is the value of the digit 7 in the number 478,932?

Solution:
Step 1: Write the number: 478,932.

Step 2: The digits are 4, 7, 8, 9, 3, and 2. The 7 is in the ten-thousands place (fifth from the right).

Step 3: The value of 7 in the ten-thousands place is 7 × 10,000 = 70,000.

Answer: The value of 7 is 70,000.
Example 2: Building a Number
Problem: What number has 5 hundred-thousands, 2 ten-thousands, 8 thousands, 3 hundreds, 6 tens, and 9 ones?

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

Step 2: Write the ten-thousands digit: 2.

Step 3: Write the thousands digit: 8.

Step 4: Write the hundreds digit: 3.

Step 5: Write the tens digit: 6.

Step 6: Write the ones digit: 9.

Step 7: Combine: 528,369.

Answer: The number is 528,369.
Watch Out!
Remember that the value of a digit depends on its position. The digit 3 in 345,678 has a value of 300,000, while in 534,678 it has a value of 30,000.

Practice for Place Value

  1. What is the value of the digit 6 in 613,492?
  2. What number has 8 hundred-thousands, 0 ten-thousands, 4 thousands, 2 hundreds, 5 tens, and 7 ones?
  3. In the number 900,415, what digit is in the hundreds place?
  4. What is the value of the digit 9 in 29,870?
  5. Write the number with 7 hundred-thousands, 3 ten-thousands, 0 thousands, 8 hundreds, 7 tens, and 6 ones.

Reading Numbers in Words

To read a 5-6 digit number in words, read the part before the comma as one number and say "thousand", then read the remaining three digits. For 6-digit numbers, read the hundred-thousands, ten-thousands, and thousands as one number before "thousand", then the remaining three digits.

Step-by-Step: Reading a 5-6 Digit Number
1. Read the digits before the first comma (the thousands part) as one number and say "thousand".
2. Read the remaining three digits as a 3-digit number.
3. For numbers like 345,000, say "three hundred forty-five thousand".
4. For numbers like 600,000, say "six hundred 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: 482,736; 605,000; 990,004.

Solution:
Step 1: 482,736 = four hundred eighty-two thousand seven hundred thirty-six.

Step 2: 605,000 = six hundred five thousand.

Step 3: 990,004 = nine hundred ninety thousand four.

Answer: 482,736 = four hundred eighty-two thousand seven hundred thirty-six; 605,000 = six hundred five thousand; 990,004 = nine hundred ninety thousand four.
Example 4: Writing Numbers from Words
Problem: Write the following as numbers: seven hundred twenty-three thousand four hundred fifty-six, eight hundred thousand two, five hundred sixty-seven thousand eight hundred.

Solution:
Step 1: seven hundred twenty-three thousand four hundred fifty-six = 723,456.

Step 2: eight hundred thousand two = 800,002.

Step 3: five hundred sixty-seven thousand eight hundred = 567,800.

Answer: 723,456; 800,002; 567,800.
Watch Out!
When reading numbers with zeros, be careful not to say "and" (e.g., 800,002 is "eight hundred thousand two", not "eight hundred thousand and two").

Practice for Reading Numbers in Words

  1. Write 621,895 in words.
  2. Write 900,040 in words.
  3. Write 710,005 in words.
  4. Write "three hundred fifty-five thousand eight hundred twenty-one" as a number.
  5. Write "four hundred thirty-three thousand five" as a number.

Writing Numbers in Expanded Form

Expanded form shows the value of each digit in a number. For a 5-6 digit number, it is the sum of the hundred-thousands, ten-thousands, thousands, hundreds, tens, and ones values.

Step-by-Step: Writing in Expanded Form
1. Identify the hundred-thousands digit and multiply it by 100,000.
2. Identify the ten-thousands digit and multiply it by 10,000.
3. Identify the thousands digit and multiply it by 1,000.
4. Identify the hundreds digit and multiply it by 100.
5. Identify the tens digit and multiply it by 10.
6. Identify the ones digit.
7. Write the sum of these six values.
Example 5: Expanded Form (6-Digit)
Problem: Write 836,572 in expanded form.

Solution:
Step 1: Hundred-thousands digit is 8 → 8 × 100,000 = 800,000.

Step 2: Ten-thousands digit is 3 → 3 × 10,000 = 30,000.

Step 3: Thousands digit is 6 → 6 × 1,000 = 6,000.

Step 4: Hundreds digit is 5 → 5 × 100 = 500.

Step 5: Tens digit is 7 → 7 × 10 = 70.

Step 6: Ones digit is 2 → 2.

Step 7: Sum: 800,000 + 30,000 + 6,000 + 500 + 70 + 2.

Answer: 836,572 = 800,000 + 30,000 + 6,000 + 500 + 70 + 2.
Example 6: Expanded Form (5-Digit)
Problem: Write 90,045 in expanded form.

Solution:
Step 1: Ten-thousands digit is 9 → 9 × 10,000 = 90,000.

Step 2: Thousands digit is 0 → 0 × 1,000 = 0.

Step 3: Hundreds digit is 0 → 0 × 100 = 0.

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

Step 5: Ones digit is 5 → 5.

Step 6: Sum: 90,000 + 0 + 0 + 40 + 5.

Answer: 90,045 = 90,000 + 0 + 0 + 40 + 5.
Watch Out!
Make sure to include zeros in expanded form if a digit is zero. For example, 400,502 = 400,000 + 0 + 0 + 500 + 0 + 2.

Practice for Expanded Form

  1. Write 562,438 in expanded form.
  2. Write 700,406 in expanded form.
  3. Write 91,100 in expanded form.
  4. What number is 400,000 + 30,000 + 2,000 + 500 + 60 + 7?
  5. What number is 800,000 + 0 + 0 + 700 + 0 + 3?

Comparing & Ordering Numbers

To compare 5-6 digit numbers, compare the hundred-thousands digits first. If they are equal, compare the ten-thousands digits, then thousands, hundreds, tens, and ones. Use symbols: > (greater than), < (less than), = (equal to).

Step-by-Step: Comparing Numbers
1. Compare the hundred-thousands digits. The larger digit means the number is larger.
2. If the hundred-thousands digits are equal, compare the ten-thousands digits.
3. If the ten-thousands digits are also equal, compare the thousands digits.
4. Continue with hundreds, then tens, then ones.
5. Use <, >, or = to show the relationship.
Example 7: Comparing Numbers
Problem: Compare 456,789 and 456,798.

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

Step 2: Both have 5 in the ten-thousands place.

Step 3: Both have 6 in the thousands place.

Step 4: Compare hundreds: 7 vs 7 (equal).

Step 5: Compare tens: 8 vs 9. 8 is less than 9, so 456,789 < 456,798.

Answer: 456,789 < 456,798.
Example 8: Ordering Numbers
Problem: Order these numbers from least to greatest: 389,756; 390,012; 389,750; 391,100.

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

Step 2: Compare ten-thousands: 389,xxx and 390,xxx. So 389,xxx < 390,xxx < 391,100.

Step 3: For 389,xxx: compare thousands: 9 vs 9 (equal). Compare hundreds: 7 vs 7 (equal). Compare tens: 5 vs 5 (equal). Compare ones: 6 vs 0. 389,750 < 389,756.

Step 4: Order: 389,750; 389,756; 390,012; 391,100.

Answer: 389,750; 389,756; 390,012; 391,100.
Watch Out!
When comparing numbers, always start with the highest place value (hundred-thousands). Do not compare ones digits first!

Practice for Comparing & Ordering

  1. Compare: 612,345 ☐ 612,354 (use >, <, or =)
  2. Compare: 800,070 ☐ 800,700
  3. Compare: 999,999 ☐ 999,998
  4. Order these from greatest to least: 456,000; 456,500; 455,999; 456,001.
  5. Order these from least to greatest: 123,456; 123,654; 123,546; 123,465.

Rounding Large Numbers

Rounding helps us estimate large numbers quickly. To round a number, look at the digit to the right of the place you are rounding to. If it is 5 or more, round up; if it is 4 or less, round down.

Step-by-Step: Rounding Numbers
1. Identify the place value you are rounding to (e.g., nearest thousand).
2. Look at the digit to the right of that place.
3. If that digit is 5 or more, add 1 to the rounding digit and change all digits to the right to zero.
4. If that digit is 4 or less, keep the rounding digit the same and change all digits to the right to zero.
Example 9: Rounding to the Nearest Thousand
Problem: Round 345,678 to the nearest thousand.

Solution:
Step 1: Identify the thousands place: 5 (in 345,678).

Step 2: Look at the digit to the right (hundreds place): 6.

Step 3: 6 is 5 or more, so round up: 5 becomes 6.

Step 4: Change all digits to the right to zero: 346,000.

Answer: 345,678 rounded to the nearest thousand is 346,000.
Example 10: Rounding to the Nearest Ten-Thousand
Problem: Round 782,345 to the nearest ten-thousand.

Solution:
Step 1: Identify the ten-thousands place: 8 (in 782,345).

Step 2: Look at the digit to the right (thousands place): 2.

Step 3: 2 is 4 or less, so round down: 8 stays 8.

Step 4: Change all digits to the right to zero: 780,000.

Answer: 782,345 rounded to the nearest ten-thousand is 780,000.
Watch Out!
When rounding, remember to change all digits to the right of the rounding place to zero. Do not forget the zeros!

Practice for Rounding

  1. Round 456,789 to the nearest thousand.
  2. Round 234,567 to the nearest ten-thousand.
  3. Round 899,999 to the nearest hundred-thousand.
  4. Round 1,000,000 to the nearest million (think about what happens).
  5. Round 345,678 to the nearest hundred.

Cumulative Practice Exercises

  1. What is the value of the digit 9 in 934,278?
  2. Write 745,206 in words.
  3. Write 800,030 in expanded form.
  4. Compare: 654,321 ☐ 654,312 (use >, <, or =)
  5. Order these numbers from least to greatest: 234,567; 234,657; 234,576; 234,765.
  6. What number is 600,000 + 40,000 + 3,000 + 200 + 70 + 8?
  7. Write "eight hundred ninety-nine thousand five hundred seventy-one" as a number.
  8. What is the value of the digit 4 in 746,823?
  9. Write 900,017 in expanded form.
  10. Compare: 830,001 ☐ 830,010 (use >, <, or =)
  11. Order these from greatest to least: 555,555; 555,505; 555,550; 555,500.
  12. What number has 7 hundred-thousands, 2 ten-thousands, 8 thousands, 0 hundreds, 7 tens, and 4 ones?
  13. Write 123,045 in words.
  14. What is the value of the digit 6 in 167,895?
  15. Compare: 999,999 ☐ 1,000,000 (use >, <, or =)
  16. Round 234,567 to the nearest thousand.
  17. Round 789,123 to the nearest ten-thousand.
  18. Round 456,789 to the nearest hundred-thousand.
  19. Round 123,456 to the nearest hundred.
  20. Round 999,999 to the nearest thousand.
Show/Hide Answers

Solutions to Cumulative Exercises

  1. Step 1: In 934,278, the 9 is in the hundred-thousands place.
    Answer: 900,000.
  2. Step 1: 745,206 = seven hundred forty-five thousand two hundred six.
    Answer: seven hundred forty-five thousand two hundred six.
  3. Step 1: 800,030 = 800,000 + 0 + 0 + 0 + 30 + 0.
    Answer: 800,000 + 0 + 0 + 0 + 30 + 0.
  4. Step 1: 654,321 vs 654,312: hundred-thousands same (6), ten-thousands same (5), thousands same (4), hundreds same (3), tens: 2 vs 1. 654,321 > 654,312.
    Answer: 654,321 > 654,312.
  5. Step 1: All in the 234,000s. Order: 234,567; 234,576; 234,657; 234,765.
    Answer: 234,567; 234,576; 234,657; 234,765.
  6. Step 1: 600,000 + 40,000 + 3,000 + 200 + 70 + 8 = 643,278.
    Answer: 643,278.
  7. Step 1: eight hundred ninety-nine thousand = 899,000; five hundred seventy-one = 571.
    Answer: 899,571.
  8. Step 1: In 746,823, the 4 is in the ten-thousands place.
    Answer: 40,000.
  9. Step 1: 900,017 = 900,000 + 0 + 0 + 0 + 10 + 7.
    Answer: 900,000 + 0 + 0 + 0 + 10 + 7.
  10. Step 1: 830,001 vs 830,010: hundred-thousands same (8), ten-thousands same (3), thousands same (0), hundreds same (0), tens: 0 vs 1. 830,001 < 830,010.
    Answer: 830,001 < 830,010.
  11. Step 1: All in the 555,000s. Order: 555,555; 555,550; 555,505; 555,500.
    Answer: 555,555; 555,550; 555,505; 555,500.
  12. Step 1: 7 hundred-thousands = 700,000; 2 ten-thousands = 20,000; 8 thousands = 8,000; 0 hundreds = 0; 7 tens = 70; 4 ones = 4.
    Answer: 728,074.
  13. Step 1: 123,045 = one hundred twenty-three thousand forty-five.
    Answer: one hundred twenty-three thousand forty-five.
  14. Step 1: In 167,895, the 6 is in the ten-thousands place.
    Answer: 60,000.
  15. Step 1: 999,999 vs 1,000,000: compare hundred-thousands: 9 vs 1 (with carry). 999,999 < 1,000,000.
    Answer: 999,999 < 1,000,000.
  16. Step 1: 234,567 rounded to nearest thousand: thousands digit is 4, look at hundreds: 5 (round up). 234,000 + 1,000 = 235,000.
    Answer: 235,000.
  17. Step 1: 789,123 rounded to nearest ten-thousand: ten-thousands digit is 8, look at thousands: 9 (round up). 789,000 + 10,000 = 790,000.
    Answer: 790,000.
  18. Step 1: 456,789 rounded to nearest hundred-thousand: hundred-thousands digit is 4, look at ten-thousands: 5 (round up). 456,000 + 100,000 = 500,000.
    Answer: 500,000.
  19. Step 1: 123,456 rounded to nearest hundred: hundreds digit is 4, look at tens: 5 (round up). 123,400 + 100 = 123,500.
    Answer: 123,500.
  20. Step 1: 999,999 rounded to nearest thousand: thousands digit is 9, look at hundreds: 9 (round up). 999,000 + 1,000 = 1,000,000.
    Answer: 1,000,000.

Conclusion & Summary

Reading and writing 5-6 digit numbers is an essential skill for everyday math. By understanding place value up to the hundred-thousands, you can read any number up to 999,999, write it in expanded form, compare numbers, and round them. These skills will help you with addition, subtraction, and more advanced math topics involving large numbers.

Key Takeaways:
1. Place Value: 5-6 digit numbers have hundred-thousands, ten-thousands, thousands, hundreds, tens, and ones places.
2. Reading: Say the hundred-thousands, ten-thousands, and thousands, then "thousand", then the remaining three digits.
3. Expanded Form: 345,678 = 300,000 + 40,000 + 5,000 + 600 + 70 + 8.
4. Comparing: Compare hundred-thousands first, then ten-thousands, thousands, hundreds, tens, and ones.
5. Rounding: Look at the digit to the right of the rounding place; 5 or more rounds up.

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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