What is Expanded Form of a Number?

S3-SA4-0012

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

The expanded form of a number is a way of writing it that shows the value of each digit. It breaks down a number into the sum of its place values, like ones, tens, hundreds, and so on. This helps us understand the true worth of each digit in the number.

Simple Example

Quick Example

Imagine your cricket team scored 245 runs. In expanded form, 245 is not just two, four, five. It means 2 hundreds, 4 tens, and 5 ones. So, it's 200 + 40 + 5. This shows how each digit contributes to the total score.

Worked Example

Step-by-Step

Let's write the expanded form of the number 3,567.

Step 1: Identify the place value of each digit.
In 3,567:
Digit 3 is in the thousands place.
Digit 5 is in the hundreds place.
Digit 6 is in the tens place.
Digit 7 is in the ones place.

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Step 2: Write the value of each digit.
Value of 3 in thousands place = 3 x 1000 = 3000
Value of 5 in hundreds place = 5 x 100 = 500
Value of 6 in tens place = 6 x 10 = 60
Value of 7 in ones place = 7 x 1 = 7

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Step 3: Add these values together.
3000 + 500 + 60 + 7

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Answer: The expanded form of 3,567 is 3000 + 500 + 60 + 7.

Why It Matters

Understanding expanded form is super useful for many advanced fields! In Computer Science, it helps in understanding how computers store and process large numbers. Data Scientists use similar logic to analyze huge datasets, and even in Cryptography, breaking down numbers is key to securing information. It's a foundational skill for future tech leaders!

Common Mistakes

MISTAKE: Writing only the digits instead of their place values (e.g., for 456, writing 4 + 5 + 6). | CORRECTION: Always multiply each digit by its place value (e.g., 400 + 50 + 6).

MISTAKE: Forgetting to include zeros for missing place values (e.g., for 708, writing 700 + 8, ignoring the tens place). | CORRECTION: If a place value has a 0, its value is 0, but it still represents that place (e.g., 700 + 0 + 8).

MISTAKE: Confusing expanded form with word form (e.g., writing 'three thousand five hundred sixty-seven' instead of 3000 + 500 + 60 + 7). | CORRECTION: Expanded form uses numbers and addition signs, not words.

Practice Questions

Try It Yourself

QUESTION: Write the expanded form of 89. | ANSWER: 80 + 9

QUESTION: What is the expanded form of 5,023? | ANSWER: 5000 + 0 + 20 + 3 (or 5000 + 20 + 3)

QUESTION: A mobile phone costs Rs. 12,349. Write this amount in expanded form. | ANSWER: 10000 + 2000 + 300 + 40 + 9

MCQ

Quick Quiz

Which of the following is the expanded form of 670?

6 + 7 + 0

60 + 70 + 0

600 + 70 + 0

6000 + 700 + 0

The Correct Answer Is:

The digit 6 is in the hundreds place (6 x 100 = 600), the digit 7 is in the tens place (7 x 10 = 70), and 0 is in the ones place (0 x 1 = 0). So, 600 + 70 + 0 is the correct expanded form.

Real World Connection

In the Real World

When you check your bank balance or see the price of an item online, like on Flipkart or Amazon, the numbers you see are actually a compact way of writing their expanded form. For example, if your bank balance is Rs. 15,750, it means Rs. 10,000 + Rs. 5,000 + Rs. 700 + Rs. 50 + Rs. 0. Understanding this helps you grasp the true value and breakdown of money.

Key Vocabulary

Key Terms

PLACE VALUE: The position of a digit in a number that tells its value (e.g., ones, tens, hundreds). | DIGIT: A single symbol used to make numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). | SUM: The result of adding two or more numbers. | EXPANDED FORM: A way to write a number by adding the value of each of its digits.

What's Next

What to Learn Next

Great job learning expanded form! Now that you understand how numbers break down, you're ready to explore 'Standard Form of a Number.' This will teach you how to convert expanded forms back into regular numbers, which is the next logical step in mastering number representation!