Skills without mastery are useless. Mastery is impossible without the right methods. BlitzGrok platform makes mastery effortless and fastest with proven, smart practice.
Skills without mastery are useless. Mastery is impossible without the right methods. BlitzGrok platform makes mastery effortless and fastest with proven, smart practice.
Three-digit numbers are numbers from 100 to 999. These numbers use three places: hundreds, tens, and ones. Understanding three-digit numbers helps you work with larger quantities and builds the foundation for understanding our number system that can extend infinitely!
A three-digit number has exactly three digits: - The first digit represents hundreds - The second digit represents tens - The third digit represents ones
Examples: - 234 is a three-digit number - 507 is a three-digit number - 999 is a three-digit number - 100 is a three-digit number
Not three-digit numbers: - 45 (only two digits) - 8 (only one digit) - 1,234 (four digits)
Learning three-digit numbers helps you: - Count higher - go beyond 99 - Understand place value - each position has meaning - See patterns - how our number system works - Solve problems - work with larger quantities - Read numbers - understand hundreds in daily life
Each position in a three-digit number has a special name and value.
Hundreds | Tens | Ones
2 | 4 | 7
This represents the number 247.
The hundreds place is the first digit from the left.
Example: In 347, the hundreds digit is 3 - This means 3 hundreds - Value: 3 × 100 = 300
The hundreds digit: - Can be 1, 2, 3, 4, 5, 6, 7, 8, or 9 - Cannot be 0 (or it wouldn't be a three-digit number!) - Represents groups of 100
The tens place is the middle digit.
Example: In 347, the tens digit is 4 - This means 4 tens - Value: 4 × 10 = 40
The tens digit: - Can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 - Represents groups of 10 - Can be zero! (Like in 305)
The ones place is the last digit on the right.
Example: In 347, the ones digit is 7 - This means 7 ones - Value: 7 × 1 = 7
The ones digit: - Can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 - Represents individual units - Can be zero! (Like in 340)
The number 347 means: - 3 hundreds = 300 - 4 tens = 40 - 7 ones = 7 - Total: 300 + 40 + 7 = 347
There's a specific way to read three-digit numbers aloud.
Format: "# hundred [and] ##"
Examples:
245 → "two hundred forty-five" - 2 hundreds → "two hundred" - 45 → "forty-five"
681 → "six hundred eighty-one" - 6 hundreds → "six hundred" - 81 → "eighty-one"
309 → "three hundred nine" - 3 hundreds → "three hundred" - 09 → "nine"
Numbers with zero in the tens place:
502 → "five hundred two" (not "five hundred zero two") 708 → "seven hundred eight" 906 → "nine hundred six"
The zero is not read aloud, but notice the gap—there are no tens!
Numbers ending in zero:
430 → "four hundred thirty" 820 → "eight hundred twenty" 560 → "five hundred sixty"
Numbers with zeros in both tens and ones:
300 → "three hundred" 700 → "seven hundred" 900 → "nine hundred"
Try reading these: - 156 → "one hundred fifty-six" - 802 → "eight hundred two" - 490 → "four hundred ninety" - 637 → "six hundred thirty-seven" - 200 → "two hundred"
You can write three-digit numbers from words or descriptions.
"Four hundred twenty-three" - "Four hundred" = 400 → hundreds digit is 4 - "Twenty-three" = 23 → tens digit is 2, ones digit is 3 - Number: 423
"Six hundred five" - "Six hundred" = 600 → hundreds digit is 6 - "Five" = 5 → ones digit is 5 - No tens mentioned → tens digit is 0 - Number: 605
"Nine hundred seventy" - "Nine hundred" = 900 → hundreds digit is 9 - "Seventy" = 70 → tens digit is 7, ones digit is 0 - Number: 970
Expanded form shows the value of each digit separately.
Example: 200 + 60 + 5 = ? - Hundreds: 200 = 2 hundreds - Tens: 60 = 6 tens - Ones: 5 = 5 ones - Number: 265
Example: 700 + 0 + 3 = ? - Hundreds: 700 = 7 hundreds - Tens: 0 = 0 tens - Ones: 3 = 3 ones - Number: 703
Example: 400 + 90 + 0 = ? - Hundreds: 400 = 4 hundreds - Tens: 90 = 9 tens - Ones: 0 = 0 ones - Number: 490
"5 hundreds, 3 tens, 8 ones" - Hundreds digit: 5 - Tens digit: 3 - Ones digit: 8 - Number: 538
"1 hundred, 0 tens, 6 ones" - Hundreds digit: 1 - Tens digit: 0 - Ones digit: 6 - Number: 106
Each digit's value depends on its position.
The same digit has different values in different positions!
Example with the digit 5: - In 523: the 5 is in the hundreds place = 500 - In 253: the 5 is in the tens place = 50 - In 325: the 5 is in the ones place = 5
The digit 5 changes value based on where it is!
Look at 444: - First 4: hundreds place = 400 - Second 4: tens place = 40 - Third 4: ones place = 4 - Total: 400 + 40 + 4 = 444
All the same digit, but different values!
Zero is special—it holds a place to show nothing is there.
Compare: - 24: Two tens and four ones = 24 - 204: Two hundreds, zero tens, four ones = 204 - 240: Two hundreds, four tens, zero ones = 240
The zeros show which places are empty!
Without zero, we couldn't tell the difference: - 305 ≠ 35 (the zero shows there are no tens) - 450 ≠ 45 (the zero shows there are no ones)
Visual models help us understand what three-digit numbers represent.
Hundreds: Large flat squares (100 small cubes) Tens: Long sticks (10 small cubes) Ones: Small individual cubes (1 cube)
Example for 234:
Hundreds (2): ▢▢
Tens (3): ▬▬▬
Ones (4): ●●●●
Total: 200 + 30 + 4 = 234
Show each place value separately:
547:
500 + 40 + 7 = 547
(5 hundreds) + (4 tens) + (7 ones)
802:
800 + 0 + 2 = 802
(8 hundreds) + (0 tens) + (2 ones)
Three-digit numbers extend the number line beyond 100:
100 ---- 200 ---- 300 ---- 400 ---- 500 ---- 600 ---- 700 ---- 800 ---- 900 ---- 1000
↑ ↑ ↑
125 500 875
From 100: - 100, 101, 102, 103, 104, 105...
Notice: Ones place changes each time!
From 100: - 100, 110, 120, 130, 140, 150...
Notice: Tens place changes each time!
From 234: - 234, 244, 254, 264, 274, 284...
From 100: - 100, 200, 300, 400, 500, 600, 700, 800, 900
Notice: Hundreds place changes each time!
From 150: - 150, 250, 350, 450, 550, 650...
Ones to tens boundary: - 127, 128, 129, 130, 131... - When ones reach 9, the next number increases tens!
Tens to hundreds boundary: - 197, 198, 199, 200, 201... - When both ones and tens reach 9, the next number increases hundreds!
Rule 1: Compare hundreds first - 425 vs 381 - 4 hundreds > 3 hundreds - 425 is bigger
Rule 2: If hundreds are equal, compare tens - 456 vs 489 - Both have 4 hundreds - 5 tens < 8 tens - 489 is bigger
Rule 3: If hundreds and tens are equal, compare ones - 672 vs 678 - Both have 6 hundreds and 7 tens - 2 ones < 8 ones - 678 is bigger
Put in order from least to greatest: 523, 235, 532, 325
Step 1: Look at hundreds - 235 has 2 hundreds (smallest) - 325 has 3 hundreds - 523 and 532 have 5 hundreds (largest)
Step 2: For numbers with same hundreds, compare tens - 523 has 2 tens - 532 has 3 tens - 532 > 523
Final order: 235, 325, 523, 532
Three-digit numbers appear everywhere in daily life!
Problem: "What is the value of the 6 in 682?"
Solution: - Position: Hundreds place (first digit) - Value: 6 × 100 = 600 - Answer: 600
Problem: "Write the number that has 4 hundreds, 0 tens, and 8 ones."
Solution: - Hundreds digit: 4 - Tens digit: 0 - Ones digit: 8 - Answer: 408
Problem: "Which is greater: 567 or 576?"
Solution: - Compare hundreds: both have 5 (equal) - Compare tens: 6 vs 7 → 7 is greater - Answer: 576 is greater
Problem: "Write 739 in expanded form."
Solution: - 7 hundreds = 700 - 3 tens = 30 - 9 ones = 9 - Answer: 700 + 30 + 9
Materials: Base-ten blocks (or drawings)
Activity: 1. Teacher calls out a number (like 346) 2. Build it using hundreds, tens, and ones blocks 3. Count: 3 hundreds, 4 tens, 6 ones 4. Write the number
Materials: Three dice, paper
Activity: 1. Roll three dice 2. First die = hundreds digit 3. Second die = tens digit 4. Third die = ones digit 5. Write the number and read it aloud 6. Write it in expanded form
Find three-digit numbers: - In books (page numbers) - On buildings (addresses) - On products (weights, volumes) - On signs (distances)
Record them and practice reading them!
Create cards: - Write digits 0-9 on cards - Draw three cards - Arrange to make the biggest number possible - Arrange to make the smallest three-digit number possible - Compare your numbers with a partner
Give clues: - "My number has 5 hundreds" - "The tens digit is 2 more than the ones digit" - "The ones digit is 3" - What's the number? (523)
Take turns creating and solving mystery numbers!
Problem: Reading 305 as "three hundred five" → writing 3005
Solution: Remember three-digit numbers only have three digits! Count the places.
Problem: Writing "six hundred eight" as 68 instead of 608
Solution: Use a place value chart. If tens aren't mentioned, write 0.
Problem: Hearing "four hundred twelve" and writing 214
Solution: Write hundreds first, then tens, then ones. Listen for "hundred" to identify the hundreds digit.
Problem: Thinking 450 and 45 are the same
Solution: Zeros matter! They show which places are empty.
You've mastered three-digit numbers when you can: - ✓ Identify the hundreds, tens, and ones digits - ✓ Read three-digit numbers correctly - ✓ Write three-digit numbers from words - ✓ Explain the value of each digit based on its position - ✓ Compare and order three-digit numbers - ✓ Write numbers in expanded form - ✓ Recognize three-digit numbers in real life
Understanding three-digit numbers prepares you for: - Four-digit numbers: Thousands place - Addition and subtraction within 1000: Larger calculations - Rounding: Estimating to nearest ten or hundred - Multi-digit multiplication and division: Operations with bigger numbers - Decimals: Understanding places to the right of ones
Three-digit numbers open up a whole new world of mathematics, allowing you to count, compare, and calculate with quantities from 100 to 999. By understanding that each position—hundreds, tens, and ones—has a specific value, you grasp the beautiful pattern of our place value system. This system can extend infinitely, but mastering three-digit numbers is a critical stepping stone. Practice identifying place values, reading and writing numbers correctly, and recognizing these numbers in your daily life. The skills you build now will support all your future work with larger numbers and more complex mathematics!
Three-digit numbers are numbers from 100 to 999. These numbers use three places: hundreds, tens, and ones. Understanding three-digit numbers helps you work with larger quantities and builds the foundation for understanding our number system that can extend infinitely!
A three-digit number has exactly three digits: - The first digit represents hundreds - The second digit represents tens - The third digit represents ones
Examples: - 234 is a three-digit number - 507 is a three-digit number - 999 is a three-digit number - 100 is a three-digit number
Not three-digit numbers: - 45 (only two digits) - 8 (only one digit) - 1,234 (four digits)
Learning three-digit numbers helps you: - Count higher - go beyond 99 - Understand place value - each position has meaning - See patterns - how our number system works - Solve problems - work with larger quantities - Read numbers - understand hundreds in daily life
Each position in a three-digit number has a special name and value.
Hundreds | Tens | Ones
2 | 4 | 7
This represents the number 247.
The hundreds place is the first digit from the left.
Example: In 347, the hundreds digit is 3 - This means 3 hundreds - Value: 3 × 100 = 300
The hundreds digit: - Can be 1, 2, 3, 4, 5, 6, 7, 8, or 9 - Cannot be 0 (or it wouldn't be a three-digit number!) - Represents groups of 100
The tens place is the middle digit.
Example: In 347, the tens digit is 4 - This means 4 tens - Value: 4 × 10 = 40
The tens digit: - Can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 - Represents groups of 10 - Can be zero! (Like in 305)
The ones place is the last digit on the right.
Example: In 347, the ones digit is 7 - This means 7 ones - Value: 7 × 1 = 7
The ones digit: - Can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 - Represents individual units - Can be zero! (Like in 340)
The number 347 means: - 3 hundreds = 300 - 4 tens = 40 - 7 ones = 7 - Total: 300 + 40 + 7 = 347
There's a specific way to read three-digit numbers aloud.
Format: "# hundred [and] ##"
Examples:
245 → "two hundred forty-five" - 2 hundreds → "two hundred" - 45 → "forty-five"
681 → "six hundred eighty-one" - 6 hundreds → "six hundred" - 81 → "eighty-one"
309 → "three hundred nine" - 3 hundreds → "three hundred" - 09 → "nine"
Numbers with zero in the tens place:
502 → "five hundred two" (not "five hundred zero two") 708 → "seven hundred eight" 906 → "nine hundred six"
The zero is not read aloud, but notice the gap—there are no tens!
Numbers ending in zero:
430 → "four hundred thirty" 820 → "eight hundred twenty" 560 → "five hundred sixty"
Numbers with zeros in both tens and ones:
300 → "three hundred" 700 → "seven hundred" 900 → "nine hundred"
Try reading these: - 156 → "one hundred fifty-six" - 802 → "eight hundred two" - 490 → "four hundred ninety" - 637 → "six hundred thirty-seven" - 200 → "two hundred"
You can write three-digit numbers from words or descriptions.
"Four hundred twenty-three" - "Four hundred" = 400 → hundreds digit is 4 - "Twenty-three" = 23 → tens digit is 2, ones digit is 3 - Number: 423
"Six hundred five" - "Six hundred" = 600 → hundreds digit is 6 - "Five" = 5 → ones digit is 5 - No tens mentioned → tens digit is 0 - Number: 605
"Nine hundred seventy" - "Nine hundred" = 900 → hundreds digit is 9 - "Seventy" = 70 → tens digit is 7, ones digit is 0 - Number: 970
Expanded form shows the value of each digit separately.
Example: 200 + 60 + 5 = ? - Hundreds: 200 = 2 hundreds - Tens: 60 = 6 tens - Ones: 5 = 5 ones - Number: 265
Example: 700 + 0 + 3 = ? - Hundreds: 700 = 7 hundreds - Tens: 0 = 0 tens - Ones: 3 = 3 ones - Number: 703
Example: 400 + 90 + 0 = ? - Hundreds: 400 = 4 hundreds - Tens: 90 = 9 tens - Ones: 0 = 0 ones - Number: 490
"5 hundreds, 3 tens, 8 ones" - Hundreds digit: 5 - Tens digit: 3 - Ones digit: 8 - Number: 538
"1 hundred, 0 tens, 6 ones" - Hundreds digit: 1 - Tens digit: 0 - Ones digit: 6 - Number: 106
Each digit's value depends on its position.
The same digit has different values in different positions!
Example with the digit 5: - In 523: the 5 is in the hundreds place = 500 - In 253: the 5 is in the tens place = 50 - In 325: the 5 is in the ones place = 5
The digit 5 changes value based on where it is!
Look at 444: - First 4: hundreds place = 400 - Second 4: tens place = 40 - Third 4: ones place = 4 - Total: 400 + 40 + 4 = 444
All the same digit, but different values!
Zero is special—it holds a place to show nothing is there.
Compare: - 24: Two tens and four ones = 24 - 204: Two hundreds, zero tens, four ones = 204 - 240: Two hundreds, four tens, zero ones = 240
The zeros show which places are empty!
Without zero, we couldn't tell the difference: - 305 ≠ 35 (the zero shows there are no tens) - 450 ≠ 45 (the zero shows there are no ones)
Visual models help us understand what three-digit numbers represent.
Hundreds: Large flat squares (100 small cubes) Tens: Long sticks (10 small cubes) Ones: Small individual cubes (1 cube)
Example for 234:
Hundreds (2): ▢▢
Tens (3): ▬▬▬
Ones (4): ●●●●
Total: 200 + 30 + 4 = 234
Show each place value separately:
547:
500 + 40 + 7 = 547
(5 hundreds) + (4 tens) + (7 ones)
802:
800 + 0 + 2 = 802
(8 hundreds) + (0 tens) + (2 ones)
Three-digit numbers extend the number line beyond 100:
100 ---- 200 ---- 300 ---- 400 ---- 500 ---- 600 ---- 700 ---- 800 ---- 900 ---- 1000
↑ ↑ ↑
125 500 875
From 100: - 100, 101, 102, 103, 104, 105...
Notice: Ones place changes each time!
From 100: - 100, 110, 120, 130, 140, 150...
Notice: Tens place changes each time!
From 234: - 234, 244, 254, 264, 274, 284...
From 100: - 100, 200, 300, 400, 500, 600, 700, 800, 900
Notice: Hundreds place changes each time!
From 150: - 150, 250, 350, 450, 550, 650...
Ones to tens boundary: - 127, 128, 129, 130, 131... - When ones reach 9, the next number increases tens!
Tens to hundreds boundary: - 197, 198, 199, 200, 201... - When both ones and tens reach 9, the next number increases hundreds!
Rule 1: Compare hundreds first - 425 vs 381 - 4 hundreds > 3 hundreds - 425 is bigger
Rule 2: If hundreds are equal, compare tens - 456 vs 489 - Both have 4 hundreds - 5 tens < 8 tens - 489 is bigger
Rule 3: If hundreds and tens are equal, compare ones - 672 vs 678 - Both have 6 hundreds and 7 tens - 2 ones < 8 ones - 678 is bigger
Put in order from least to greatest: 523, 235, 532, 325
Step 1: Look at hundreds - 235 has 2 hundreds (smallest) - 325 has 3 hundreds - 523 and 532 have 5 hundreds (largest)
Step 2: For numbers with same hundreds, compare tens - 523 has 2 tens - 532 has 3 tens - 532 > 523
Final order: 235, 325, 523, 532
Three-digit numbers appear everywhere in daily life!
Problem: "What is the value of the 6 in 682?"
Solution: - Position: Hundreds place (first digit) - Value: 6 × 100 = 600 - Answer: 600
Problem: "Write the number that has 4 hundreds, 0 tens, and 8 ones."
Solution: - Hundreds digit: 4 - Tens digit: 0 - Ones digit: 8 - Answer: 408
Problem: "Which is greater: 567 or 576?"
Solution: - Compare hundreds: both have 5 (equal) - Compare tens: 6 vs 7 → 7 is greater - Answer: 576 is greater
Problem: "Write 739 in expanded form."
Solution: - 7 hundreds = 700 - 3 tens = 30 - 9 ones = 9 - Answer: 700 + 30 + 9
Materials: Base-ten blocks (or drawings)
Activity: 1. Teacher calls out a number (like 346) 2. Build it using hundreds, tens, and ones blocks 3. Count: 3 hundreds, 4 tens, 6 ones 4. Write the number
Materials: Three dice, paper
Activity: 1. Roll three dice 2. First die = hundreds digit 3. Second die = tens digit 4. Third die = ones digit 5. Write the number and read it aloud 6. Write it in expanded form
Find three-digit numbers: - In books (page numbers) - On buildings (addresses) - On products (weights, volumes) - On signs (distances)
Record them and practice reading them!
Create cards: - Write digits 0-9 on cards - Draw three cards - Arrange to make the biggest number possible - Arrange to make the smallest three-digit number possible - Compare your numbers with a partner
Give clues: - "My number has 5 hundreds" - "The tens digit is 2 more than the ones digit" - "The ones digit is 3" - What's the number? (523)
Take turns creating and solving mystery numbers!
Problem: Reading 305 as "three hundred five" → writing 3005
Solution: Remember three-digit numbers only have three digits! Count the places.
Problem: Writing "six hundred eight" as 68 instead of 608
Solution: Use a place value chart. If tens aren't mentioned, write 0.
Problem: Hearing "four hundred twelve" and writing 214
Solution: Write hundreds first, then tens, then ones. Listen for "hundred" to identify the hundreds digit.
Problem: Thinking 450 and 45 are the same
Solution: Zeros matter! They show which places are empty.
You've mastered three-digit numbers when you can: - ✓ Identify the hundreds, tens, and ones digits - ✓ Read three-digit numbers correctly - ✓ Write three-digit numbers from words - ✓ Explain the value of each digit based on its position - ✓ Compare and order three-digit numbers - ✓ Write numbers in expanded form - ✓ Recognize three-digit numbers in real life
Understanding three-digit numbers prepares you for: - Four-digit numbers: Thousands place - Addition and subtraction within 1000: Larger calculations - Rounding: Estimating to nearest ten or hundred - Multi-digit multiplication and division: Operations with bigger numbers - Decimals: Understanding places to the right of ones
Three-digit numbers open up a whole new world of mathematics, allowing you to count, compare, and calculate with quantities from 100 to 999. By understanding that each position—hundreds, tens, and ones—has a specific value, you grasp the beautiful pattern of our place value system. This system can extend infinitely, but mastering three-digit numbers is a critical stepping stone. Practice identifying place values, reading and writing numbers correctly, and recognizing these numbers in your daily life. The skills you build now will support all your future work with larger numbers and more complex mathematics!