Place Value of 3-Digit Numbers
Place value tells us the value of each digit in a number based on its position. In a 3-digit number, each digit sits in one of three places: hundreds, tens, or ones.
For example, in the number 527, the digit 5 is worth 500, the digit 2 is worth 20, and the digit 7 is worth 7. Understanding place value is essential for reading numbers, comparing numbers, and performing addition and subtraction.
What is Place Value of 3-Digit Numbers - Class 3 Maths (Numbers up to 1000)?
The place value of a digit is the value it represents based on its position in the number.
| Place | Position | Value of each unit |
|---|---|---|
| Hundreds | First (leftmost) | 100 |
| Tens | Second (middle) | 10 |
| Ones | Third (rightmost) | 1 |
Face value is the digit itself, regardless of position. Place value = Face value x Value of the place.
Place Value = Digit x Value of its Position
Place Value of 3-Digit Numbers Formula
Place Value and Face Value Formulas:
Place Value of a digit = Digit × Value of its place
Face Value of a digit = The digit itself
Place values in a 3-digit number:
| Place | Value | Example (in 483) |
|---|---|---|
| Hundreds | × 100 | 4 × 100 = 400 |
| Tens | × 10 | 8 × 10 = 80 |
| Ones | × 1 | 3 × 1 = 3 |
The sum of all place values gives back the number: 400 + 80 + 3 = 483.
Types and Properties
Types of values a digit can have:
- Face Value: The digit itself. The face value of 6 is always 6, no matter where it appears.
- Place Value: The value based on position. The digit 6 in the hundreds place has a place value of 600, but in the tens place it has a place value of 60.
Place value of zero: The place value of 0 is always 0, but zero is an important placeholder. In the number 305, the zero keeps 3 in the hundreds place.
Solved Examples
Example 1: Finding Place Values in a Number
Question: Write the place value of each digit in 683.
Think:
- 6 is in the hundreds place → 6 × 100 = 600
- 8 is in the tens place → 8 × 10 = 80
- 3 is in the ones place → 3 × 1 = 3
Answer: Place values are 600, 80, and 3.
Example 2: Place Value of Zero
Question: What is the place value of 0 in the number 409?
Think:
- 4 is in the hundreds place → 400
- 0 is in the tens place → 0 × 10 = 0
- 9 is in the ones place → 9
Answer: The place value of 0 in 409 is 0. Zero acts as a placeholder to keep 4 in the hundreds place.
Example 3: Face Value vs Place Value
Question: In the number 372, find the face value and place value of 7.
Think:
- Face value of 7 = 7 (the digit itself)
- 7 is in the tens place
- Place value of 7 = 7 × 10 = 70
Answer: Face value = 7, Place value = 70.
Example 4: Place Value Chart
Question: Complete the place value chart for 845.
| Hundreds | Tens | Ones |
|---|---|---|
| 8 | 4 | 5 |
Think:
- 8 hundreds = 800
- 4 tens = 40
- 5 ones = 5
- 800 + 40 + 5 = 845
Answer: 845 = 800 + 40 + 5.
Example 5: Word Problem — Collecting Stamps
Question: Ria has a stamp collection. She has 2 hundreds, 9 tens, and 6 ones. How many stamps does Ria have?
Think:
- 2 hundreds = 200
- 9 tens = 90
- 6 ones = 6
- 200 + 90 + 6 = 296
Answer: Ria has 296 stamps.
Example 6: Identifying the Digit at a Given Place
Question: In the number 517, which digit is in the tens place?
Think:
- 5 → hundreds place
- 1 → tens place
- 7 → ones place
Answer: The digit in the tens place is 1.
Example 7: Same Digit, Different Places
Question: The digit 5 appears in both 523 and 350. What is its place value in each?
Think:
- In 523: 5 is in the hundreds place → 5 × 100 = 500
- In 350: 5 is in the tens place → 5 × 10 = 50
Answer: Place value of 5 in 523 is 500. Place value of 5 in 350 is 50.
Example 8: Sum of Place Values
Question: Find the sum of the place values of all digits in 746.
Think:
- Place value of 7 = 700
- Place value of 4 = 40
- Place value of 6 = 6
- Sum = 700 + 40 + 6 = 746
Answer: The sum of place values is 746. (The sum of place values of all digits always equals the number itself.)
Example 9: Word Problem — Cricket Runs
Question: In a cricket match, India scored 358 runs. What is the place value of the digit 5 in the score?
Think:
- 3 is in the hundreds place
- 5 is in the tens place → 5 × 10 = 50
- 8 is in the ones place
Answer: The place value of 5 in 358 is 50.
Example 10: Building a Number from Place Values
Question: A number has place values 200, 60, and 3. What is the number?
Think:
- 200 → digit 2 in hundreds place
- 60 → digit 6 in tens place
- 3 → digit 3 in ones place
- 200 + 60 + 3 = 263
Answer: The number is 263.
Real-World Applications
Where is place value used?
- Reading numbers: To read 572 correctly as 'five hundred seventy-two', you need to know that 5 is in the hundreds place, 7 in the tens place, and 2 in the ones place.
- Writing cheques: When adults write cheques or fill in bank forms, they write both the numeral and the number name. Place value ensures accuracy. Writing ₹508 correctly requires knowing there are 0 tens.
- Addition and subtraction: When you add 347 + 258, you line up hundreds under hundreds, tens under tens, and ones under ones. This is place value in action.
- Comparing prices: When Aditi compares the price of two school bags (₹475 vs ₹523), she first looks at the hundreds digit to decide which is more expensive.
- Measuring: A bottle holds 750 ml of water. The digit 7 represents 700 ml, the digit 5 represents 50 ml. Understanding place value helps in measurement.
Place value is the foundation of our number system. Without it, the digits 3, 5, and 2 could mean 352, 325, 235, 253, 523, or 532 — six different numbers from the same three digits!
Key Points to Remember
- Place value depends on the position of a digit in the number.
- In a 3-digit number: hundreds place (×100), tens place (×10), ones place (×1).
- Face value is the digit itself; place value = digit × position value.
- The place value of 0 is always 0, but 0 acts as a placeholder.
- The same digit can have different place values in different numbers.
- The sum of place values of all digits in a number equals the number itself.
Practice Problems
- Write the place value of each digit in 493.
- What is the place value of 6 in 604?
- In the number 888, what is the place value of each 8?
- Kavi has 4 hundreds, 0 tens, and 7 ones. What number does he have?
- Find the face value and place value of 9 in 192.
- A number has place values 300, 50, and 0. What is the number?
- Which digit has the highest place value in 654?
Frequently Asked Questions
Q1. What is place value in simple words?
Place value is the value a digit gets because of its position in a number. For example, 4 in the hundreds place means 400, but 4 in the ones place means just 4.
Q2. What is the difference between place value and face value?
Face value is the digit itself (e.g., 3 always has face value 3). Place value depends on position (e.g., 3 in the tens place has place value 30, but 3 in the hundreds place has place value 300).
Q3. What is the place value of 0?
The place value of 0 is always 0 regardless of its position. However, 0 is important as a placeholder. In 305, the 0 holds the tens place so that 3 stays in the hundreds place.
Q4. How many places does a 3-digit number have?
A 3-digit number has three places: hundreds (leftmost), tens (middle), and ones (rightmost).
Q5. Can two digits in the same number have the same place value?
No. Each position has a unique value (100, 10, or 1). But if two positions have the same digit, like 8 in 808, they still have different place values (800 and 8).
Q6. Why is place value important?
Place value helps us read and write numbers correctly, compare numbers, and perform addition, subtraction, and multiplication. Without it, we could not tell the difference between 35 and 53.
Q7. What is the place value of the leftmost digit in a 3-digit number?
The leftmost digit is in the hundreds place. Its place value is the digit multiplied by 100. For instance, in 728, the leftmost digit 7 has a place value of 700.
Q8. How do you find the place value of a digit?
Identify the position of the digit (hundreds, tens, or ones). Multiply the digit by the value of its position. For example, 6 in the tens place has a place value of 6 × 10 = 60.
