Expanded Form of 3-Digit Numbers
The expanded form of a number shows the value of each digit written as a sum. It breaks a number into hundreds, tens, and ones.
For example, 356 in expanded form is 300 + 50 + 6. Writing numbers in expanded form helps students understand place value and how each digit contributes to the total value of the number.
What is Expanded Form of 3-Digit Numbers - Class 3 Maths (Numbers up to 1000)?
The expanded form of a number is a way of writing it as the sum of the place values of each digit.
Expanded Form: 475 = 400 + 70 + 5
| Number | Hundreds | Tens | Ones | Expanded Form |
|---|---|---|---|---|
| 356 | 300 | 50 | 6 | 300 + 50 + 6 |
| 820 | 800 | 20 | 0 | 800 + 20 + 0 |
| 109 | 100 | 0 | 9 | 100 + 0 + 9 |
Standard form (also called short form) is the normal way of writing a number: 356.
Expanded Form of 3-Digit Numbers Formula
To write a number in expanded form:
- Find the place value of the hundreds digit.
- Find the place value of the tens digit.
- Find the place value of the ones digit.
- Write them as a sum: Hundreds value + Tens value + Ones value.
Solved Examples
Example 1: Basic Expanded Form
Question: Write 594 in expanded form.
Think:
- 5 hundreds = 500
- 9 tens = 90
- 4 ones = 4
Answer: 594 = 500 + 90 + 4
Example 2: Expanded Form with Zero in Tens Place
Question: Write 706 in expanded form.
Think:
- 7 hundreds = 700
- 0 tens = 0
- 6 ones = 6
Answer: 706 = 700 + 0 + 6 (or simply 700 + 6)
Example 3: Expanded Form with Zero in Ones Place
Question: Write 340 in expanded form.
Think:
- 3 hundreds = 300
- 4 tens = 40
- 0 ones = 0
Answer: 340 = 300 + 40 + 0 (or simply 300 + 40)
Example 4: Standard Form from Expanded Form
Question: Write the standard form of 200 + 30 + 8.
Think:
- 200 → 2 in hundreds place
- 30 → 3 in tens place
- 8 → 8 in ones place
- 200 + 30 + 8 = 238
Answer: The standard form is 238.
Example 5: Word Problem — Mangoes in Crates
Question: A mango seller has 4 crates of 100 mangoes, 6 bags of 10 mangoes, and 3 loose mangoes. Write the total number of mangoes in expanded form and standard form.
Think:
- 4 crates of 100 = 400
- 6 bags of 10 = 60
- 3 loose = 3
- Expanded form: 400 + 60 + 3
- Standard form: 463
Answer: Expanded form = 400 + 60 + 3; Standard form = 463.
Example 6: Expanded Form of a Round Number
Question: Write 500 in expanded form.
Think:
- 5 hundreds = 500
- 0 tens = 0
- 0 ones = 0
Answer: 500 = 500 + 0 + 0 (or simply 500)
Example 7: Matching Expanded Form to Standard Form
Question: Which number is 600 + 10 + 7?
Think:
- Add: 600 + 10 + 7 = 617
Answer: 617
Example 8: Word Problem — School Books
Question: Aditi's school library received 100 + 100 + 100 + 40 + 5 new books. Write this in standard form.
Think:
- 100 + 100 + 100 = 300
- 300 + 40 = 340
- 340 + 5 = 345
Answer: The library received 345 new books.
Example 9: Finding Missing Value in Expanded Form
Question: 862 = 800 + ___ + 2. What is the missing value?
Think:
- 862 = 800 + ? + 2
- 862 − 800 − 2 = 60
- The tens place value is 60
Answer: The missing value is 60.
Example 10: Word Problem — Auto-Rickshaw Distance
Question: Dev's auto-rickshaw travels 900 + 70 + 8 metres. How many metres did it travel? Write in standard form.
Think:
- 900 + 70 + 8 = 978
Answer: The auto-rickshaw travelled 978 metres.
Real-World Applications
Where is expanded form used?
- Understanding addition: When you add 347 + 235, you can break each number into expanded form (300 + 40 + 7) + (200 + 30 + 5) and add hundreds together (500), tens together (70), and ones together (12).
- Understanding subtraction: Expanded form helps explain borrowing. To subtract 532 − 278, write 532 = 500 + 30 + 2. Since we cannot subtract 8 from 2, we regroup 30 as 20 + 10 and add 10 to 2.
- Money calculations: If an item costs ₹475, the expanded form 400 + 70 + 5 helps you count using ₹100 notes (4 notes), ₹10 coins (7 coins), and ₹1 coins (5 coins).
- Estimation: Expanded form shows which digit contributes the most. In 867, the hundreds place (800) is the biggest part, so 867 is close to 900 when estimating.
Expanded form connects place value to arithmetic. It shows why we add column by column and how regrouping works.
Key Points to Remember
- Expanded form breaks a number into the sum of its place values.
- Example: 475 = 400 + 70 + 5.
- Standard form is the normal way of writing a number (e.g., 475).
- When a digit is 0, its place value is 0 (e.g., 306 = 300 + 0 + 6).
- To convert expanded form to standard form, add all the values together.
- To convert standard form to expanded form, find the place value of each digit.
Practice Problems
- Write 729 in expanded form.
- Write the standard form of 400 + 50 + 1.
- Write 803 in expanded form.
- Meera has 200 + 60 + 0 beads. How many beads does she have?
- Fill in the blank: 561 = ___ + 60 + 1.
- Which is greater: 300 + 80 + 2 or 300 + 70 + 9?
- Write all the 3-digit numbers whose expanded form has 0 in the tens place and uses digits 4, 0, 7.
Frequently Asked Questions
Q1. What is the expanded form of a number?
The expanded form shows a number as the sum of the place values of its digits. For example, 385 = 300 + 80 + 5.
Q2. What is the difference between expanded form and standard form?
Standard form is the normal way of writing a number (e.g., 472). Expanded form breaks it into place values (e.g., 400 + 70 + 2). Both represent the same number.
Q3. How do you write a number with zero in expanded form?
Include the zero in its place. For example, 605 = 600 + 0 + 5. You may also write it as 600 + 5, but showing the 0 makes the place value clearer.
Q4. How do you convert expanded form to standard form?
Add all the values together. For example, 700 + 20 + 3 = 723. The result is the standard form.
Q5. Why is expanded form useful?
Expanded form helps students see the value of each digit. It makes addition and subtraction with regrouping easier to understand because you can work with hundreds, tens, and ones separately.
Q6. Can a number have more than one expanded form?
The standard expanded form is unique — each number has exactly one. However, you can write 356 as 300 + 50 + 6 or as 3 hundreds + 5 tens + 6 ones. Both show the same idea.
Q7. What is the expanded form of 100?
100 = 100 + 0 + 0. It has 1 hundred, 0 tens, and 0 ones.
Q8. How is expanded form related to place value?
Expanded form is built directly from place values. Each part of the expanded form is the place value of one digit. For example, in 284, the place values 200, 80, and 4 give the expanded form 200 + 80 + 4.
