What is Expanding a Number?

S0-SA1-0576

Grade Level:

Pre-School – Class 2

All domains without exception

Definition

What is it?

Expanding a number means writing it out to show the value of each digit. It helps us understand the 'place' or position of every digit in a number, like ones, tens, hundreds, and so on. We break down the number into a sum of its parts.

Simple Example

Quick Example

Imagine you have 75 rupees. When you expand 75, it means you have 7 notes of ten rupees (70 rupees) and 5 notes of one rupee (5 rupees). So, 75 is actually 70 + 5. This shows the value of each digit clearly.

Worked Example

Step-by-Step

Let's expand the number 348.

1. Identify the place value of each digit.
- The digit 3 is in the hundreds place.
- The digit 4 is in the tens place.
- The digit 8 is in the ones place.
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2. Write the value of the digit in the hundreds place.
- 3 hundreds = 3 x 100 = 300
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3. Write the value of the digit in the tens place.
- 4 tens = 4 x 10 = 40
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4. Write the value of the digit in the ones place.
- 8 ones = 8 x 1 = 8
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5. Add these values together.
- 300 + 40 + 8
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So, the expanded form of 348 is 300 + 40 + 8.

Why It Matters

Expanding numbers is super important because it's the basic building block for understanding bigger numbers and doing calculations. It helps you grasp how our number system works, which is key for subjects like algebra and geometry. Engineers and data scientists use this understanding when working with large datasets and complex calculations.

Common Mistakes

MISTAKE: Students forget to add a zero for place values that are missing (e.g., expanding 205 as 20 + 5). | CORRECTION: Always multiply each digit by its correct place value. For 205, it's 2 hundreds + 0 tens + 5 ones, so 200 + 0 + 5.

MISTAKE: Mixing up the place values (e.g., expanding 123 as 100 + 30 + 2). | CORRECTION: Remember the order: ones, tens, hundreds, thousands, and so on, moving from right to left.

MISTAKE: Writing the digits directly instead of their value (e.g., expanding 56 as 5 + 6). | CORRECTION: Each digit's value depends on its position. 5 in 56 is 50, not just 5.

Practice Questions

Try It Yourself

QUESTION: Expand the number 67. | ANSWER: 60 + 7

QUESTION: Write the expanded form of 509. | ANSWER: 500 + 0 + 9 (or 500 + 9)

QUESTION: A cricket team scored 156 runs. Write this number in expanded form. | ANSWER: 100 + 50 + 6

MCQ

Quick Quiz

What is the expanded form of 425?

400 + 2 + 5

40 + 20 + 5

400 + 20 + 5

4 + 2 + 5

The Correct Answer Is:

The digit 4 is in the hundreds place (400), 2 is in the tens place (20), and 5 is in the ones place (5). Adding these gives 400 + 20 + 5.

Real World Connection

In the Real World

When you check your mobile data balance, say you have 1024 MB left. Understanding expanded form helps you know that it's 1 thousand MB, 0 hundreds, 2 tens, and 4 ones. This foundational idea is used by computer programmers when they work with memory addresses and data storage.

Key Vocabulary

Key Terms

PLACE VALUE: The position of a digit in a number that tells its value | ONES PLACE: The rightmost digit's position, representing single units | TENS PLACE: The second digit from the right, representing groups of ten | HUNDREDS PLACE: The third digit from the right, representing groups of one hundred | SUM: The result of adding numbers together

What's Next

What to Learn Next

Great job with expanding numbers! Next, you can learn about 'Standard Form' and 'Word Form' of numbers. These concepts build directly on expanded form and will help you read, write, and understand even larger numbers more easily.