What is Expanded Form of a Number? | Simple Explanation for Class 6

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What is the Expanded Form of a Number?

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 to show the value of each digit. It breaks down a number into the sum of its place values. For example, 345 is 300 + 40 + 5.

Simple Example

Quick Example

Imagine you collected 785 rupees from your friends for a class trip. In expanded form, this means you have 7 notes of 100 rupees, 8 notes of 10 rupees, and 5 coins of 1 rupee. So, 785 is 700 + 80 + 5.

Worked Example

Step-by-Step

Let's find the expanded form of the number 4,321.

Step 1: Identify the place value of each digit.
--- 4 is in the thousands place (value 4 x 1000 = 4000).
--- 3 is in the hundreds place (value 3 x 100 = 300).
--- 2 is in the tens place (value 2 x 10 = 20).
--- 1 is in the ones place (value 1 x 1 = 1).
--- Step 2: Write these place values as a sum.
--- 4,321 = 4000 + 300 + 20 + 1.
--- So, the expanded form of 4,321 is 4000 + 300 + 20 + 1.

Why It Matters

Understanding expanded form helps us grasp how big numbers work, which is key in fields like Data Science for managing large datasets or Computer Science for how computers store numbers. Engineers use it to design systems that handle precise measurements, and even economists analyze large financial figures using similar principles.

Common Mistakes

MISTAKE: Writing 543 as 50 + 40 + 3 | CORRECTION: Remember to consider the place value. 5 is in the hundreds place, so it's 500. The correct expanded form is 500 + 40 + 3.

MISTAKE: Ignoring zeros in the middle, e.g., writing 607 as 60 + 7 | CORRECTION: Even if a digit is zero, its place value is still part of the number. The expanded form of 607 is 600 + 0 + 7, or simply 600 + 7.

MISTAKE: Mixing up place values, e.g., writing 123 as 100 + 30 + 2 | CORRECTION: Always start from the leftmost digit and correctly identify its place value (hundreds, tens, ones, etc.). The correct expanded form for 123 is 100 + 20 + 3.

Practice Questions

Try It Yourself

QUESTION: Write the expanded form of 98. | ANSWER: 90 + 8

QUESTION: What is the expanded form of 705? | ANSWER: 700 + 0 + 5 (or 700 + 5)

QUESTION: A mobile phone costs Rs. 12,345. Write this amount in expanded form. | ANSWER: 10,000 + 2,000 + 300 + 40 + 5

MCQ

Quick Quiz

Which of the following is the expanded form of 5,678?

5000 + 600 + 7 + 8

5000 + 600 + 70 + 8

500 + 60 + 70 + 8

5 + 6 + 7 + 8

The Correct Answer Is:

Option B correctly breaks down 5,678 into its place values: 5 thousands (5000), 6 hundreds (600), 7 tens (70), and 8 ones (8). The other options incorrectly represent the place values.

Real World Connection

In the Real World

When you see the price of a new scooter, say Rs. 85,999, you are actually seeing a number made up of its place values. Understanding expanded form helps cashiers count money correctly or helps you understand how banks calculate interest on large loan amounts, where every digit's value matters.

Key Vocabulary

Key Terms

PLACE VALUE: The value of a digit based on its position in a number, like ones, tens, hundreds, etc. | 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 together. | EXPANDED FORM: Writing a number as the sum of its place values.

What's Next

What to Learn Next

Now that you understand expanded form, you're ready to explore 'Standard Form' and 'Word Form' of numbers. These concepts build directly on place value and expanded form, helping you read and write even larger numbers with ease.