What is Expanding a Number? | Simple Explanation for Class 3

S1-SA1-0022

What is Expanding a Number in Place Value?

Grade Level:

Class 3

Maths, Computing

Definition

What is it?

Expanding a number in place value means breaking down a number to show the value of each digit based on its position. It helps us understand how each digit contributes to the total value of the number. For example, in 345, the '3' means 300, the '4' means 40, and the '5' means 5.

Simple Example

Quick Example

Imagine the price of your favourite samosa is Rs. 15. If we expand 15, it means 1 ten and 5 ones. So, 10 + 5 = 15. The '1' is in the tens place, so its value is 10, and the '5' is in the ones place, so its value is 5.

Worked Example

Step-by-Step

Let's expand the number 789.

Step 1: Identify the place value of each digit. The digit '7' is in the hundreds place.
---
Step 2: The digit '8' is in the tens place.
---
Step 3: The digit '9' is in the ones place.
---
Step 4: Write the value of each digit. '7' in the hundreds place means 7 x 100 = 700.
---
Step 5: '8' in the tens place means 8 x 10 = 80.
---
Step 6: '9' in the ones place means 9 x 1 = 9.
---
Step 7: Add these values together. 700 + 80 + 9.

So, the expanded form of 789 is 700 + 80 + 9.

Why It Matters

Understanding expanded form is crucial for grasping how numbers work, which is fundamental in computing and advanced mathematics. It helps engineers design systems, and data analysts interpret large numbers, forming the base for many STEM careers.

Common Mistakes

MISTAKE: Writing the digits directly instead of their place values (e.g., expanding 345 as 3 + 4 + 5) | CORRECTION: Always multiply each digit by its place value (e.g., 300 + 40 + 5).

MISTAKE: Confusing place value with face value (e.g., saying the place value of '4' in 345 is just 4) | CORRECTION: Face value is the digit itself (4), place value is the digit multiplied by its position (4 x 10 = 40).

MISTAKE: Forgetting to include zeros for missing place values (e.g., expanding 507 as 50 + 7) | CORRECTION: Always include the zero for any missing place value (e.g., 507 expands to 500 + 0 + 7, or simply 500 + 7).

Practice Questions

Try It Yourself

QUESTION: Expand the number 245. | ANSWER: 200 + 40 + 5

QUESTION: What is the expanded form of 903? | ANSWER: 900 + 0 + 3 (or 900 + 3)

QUESTION: If a mobile data plan costs Rs. 875, how would you write 875 in expanded form? | ANSWER: 800 + 70 + 5

MCQ

Quick Quiz

Which of the following is the correct expanded form of the number 628?

6 + 2 + 8

600 + 20 + 8

60 + 20 + 8

62 + 8

The Correct Answer Is:

Option B correctly shows 6 hundreds (600), 2 tens (20), and 8 ones (8). The other options do not represent the correct place values of the digits.

Real World Connection

In the Real World

When you see your school marks, like 785 out of 1000, understanding expanded form helps you see that 785 is 7 hundreds, 8 tens, and 5 ones. This is useful for budgeting money, understanding distances on maps, or even tracking cricket scores where runs are added based on their value.

Key Vocabulary

Key Terms

PLACE VALUE: The value of a digit based on its position in a number (e.g., in 23, the place value of 2 is 20) | FACE VALUE: The value of the digit itself, regardless of its position (e.g., in 23, the face value of 2 is 2) | EXPANDED FORM: Writing a number as the sum of its digits multiplied by their place values | DIGIT: A single symbol used to make numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

What's Next

What to Learn Next

Great job learning about expanded form! Next, you can explore "Standard Form of a Number" which is the opposite process of combining the expanded form back into a single number. This will strengthen your understanding of number representation even further.