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

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What is an 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, like hundreds, tens, and ones.

Simple Example

Quick Example

Imagine your friend scored 158 runs in a cricket match. In expanded form, 158 means 100 runs (for the '1' in hundreds place) + 50 runs (for the '5' in tens place) + 8 runs (for the '8' in ones place). So, 100 + 50 + 8 is the expanded form of 158.

Worked Example

Step-by-Step

Let's write the number 7,345 in expanded form.

1. Identify the place value of each digit in 7,345.
The '7' is in the thousands place.
The '3' is in the hundreds place.
The '4' is in the tens place.
The '5' is in the ones place.
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2. Write down the value of each digit based on its place.
Value of 7: 7 x 1000 = 7000
Value of 3: 3 x 100 = 300
Value of 4: 4 x 10 = 40
Value of 5: 5 x 1 = 5
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3. Add these values together.
7000 + 300 + 40 + 5
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ANSWER: The expanded form of 7,345 is 7000 + 300 + 40 + 5.

Why It Matters

Understanding expanded form is crucial for working with large numbers in computer science and data analysis. It helps engineers design systems that process information efficiently, and it's a basic building block for understanding how complex calculations are done in fields like AI/ML and finance.

Common Mistakes

MISTAKE: Ignoring zeros in the number, e.g., writing 205 as 200 + 50 | CORRECTION: Remember that a zero in a place value means that place has a value of zero, so 205 is 200 + 0 + 5, or simply 200 + 5.

MISTAKE: Confusing place value with face value, e.g., for 345, saying the '3' has a value of 3 | CORRECTION: The 'face value' is the digit itself (3), but the 'place value' is the digit multiplied by its position (3 x 100 = 300).

MISTAKE: Incorrectly adding the place values, e.g., for 123, writing 100 + 2 + 3 | CORRECTION: Ensure each digit is multiplied by its correct place value: 100 (for 1 hundred) + 20 (for 2 tens) + 3 (for 3 ones).

Practice Questions

Try It Yourself

QUESTION: Write 48 in expanded form. | ANSWER: 40 + 8

QUESTION: What is the expanded form of the number of days in a year (assuming a non-leap year)? | ANSWER: 300 + 60 + 5

QUESTION: A mobile phone costs Rs. 12,599. Write this amount in expanded form. | ANSWER: 10000 + 2000 + 500 + 90 + 9

MCQ

Quick Quiz

Which of the following is the expanded form of 9,072?

9000 + 70 + 2

900 + 70 + 2

9000 + 700 + 2

9 + 0 + 7 + 2

The Correct Answer Is:

In 9,072, the '9' is in the thousands place (9000), '0' in hundreds place (0), '7' in tens place (70), and '2' in ones place (2). So, 9000 + 70 + 2 is correct.

Real World Connection

In the Real World

When you see your bank balance or a bill, like a bill for your electricity or internet, the amount is a number. Banks use place values and expanded forms internally to process transactions and ensure every rupee is accounted for. Even calculating total costs for your family's monthly grocery shopping uses this basic concept to add up different values correctly.

Key Vocabulary

Key Terms

PLACE VALUE: The value of a digit based on its position in a number, like ones, tens, hundreds | DIGIT: A single symbol used to make numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) | EXPANDED FORM: Writing a number as the sum of its digits' place values | FACE VALUE: The value of the digit itself, regardless of its position

What's Next

What to Learn Next

Great job understanding expanded form! Next, you can explore standard form and word form of numbers. These concepts will help you represent numbers in different ways and are super useful for understanding larger numbers and decimals.