What is Expanded Form of Decimals?

S1-SA2-0383

Grade Level:

Class 4

All STEM domains, Finance, Economics, Data Science, AI, Physics, Chemistry

Definition

What is it?

The expanded form of a decimal shows a number broken down by the value of each digit. It helps us understand what each digit (like ones, tens, tenths, hundredths) truly represents in the number.

Simple Example

Quick Example

Imagine the price of a small packet of biscuits is Rs. 12.75. In expanded form, Rs. 12.75 means 10 rupees + 2 rupees + 70 paise (or 7 tenths of a rupee) + 5 paise (or 5 hundredths of a rupee).

Worked Example

Step-by-Step

Let's write the expanded form of 34.68.

Step 1: Identify the whole number part. It is 34.

Step 2: Break down the whole number part: 3 in the tens place is 3 x 10 = 30. 4 in the ones place is 4 x 1 = 4.

Step 3: Identify the decimal part. It is .68.

Step 4: Break down the decimal part: 6 in the tenths place is 6 x (1/10) or 0.6. 8 in the hundredths place is 8 x (1/100) or 0.08.

Step 5: Combine all the parts with plus signs.

Answer: So, the expanded form of 34.68 is 30 + 4 + 0.6 + 0.08.

Why It Matters

Understanding expanded form is key for working with money, measurements, and scientific data. It's used by engineers designing structures, scientists analyzing experiments, and even financial analysts managing investments. This concept builds a strong foundation for higher math and real-world problem-solving.

Common Mistakes

MISTAKE: Writing 0.7 as 7 in the expanded form of a decimal like 5.72 | CORRECTION: Remember that digits after the decimal point represent fractions of a whole. 7 in the tenths place is 0.7, not 7.

MISTAKE: Forgetting to include the zero for a missing place value, e.g., writing 40 + 5 + 0.3 for 45.03 | CORRECTION: Even if a place value is zero, its position is important. 45.03 is 40 + 5 + 0.03 (the 0 in the tenths place means no tenths).

MISTAKE: Confusing place values, e.g., writing 0.06 for 6 in the tenths place | CORRECTION: The first digit after the decimal is tenths (0.X), the second is hundredths (0.0X), the third is thousandths (0.00X), and so on.

Practice Questions

Try It Yourself

QUESTION: Write the expanded form of 8.25. | ANSWER: 8 + 0.2 + 0.05

QUESTION: What is the expanded form of 105.7? | ANSWER: 100 + 5 + 0.7

QUESTION: A tailor bought 23.45 meters of cloth. Write this length in expanded form. | ANSWER: 20 + 3 + 0.4 + 0.05

MCQ

Quick Quiz

Which of these is the correct expanded form of 67.09?

60 + 7 + 0.9

60 + 7 + 0.09

6 + 7 + 0.09

60 + 7 + 9

The Correct Answer Is:

The number 67.09 has 6 tens (60), 7 ones (7), 0 tenths (so no 0.9), and 9 hundredths (0.09). Therefore, 60 + 7 + 0.09 is correct.

Real World Connection

In the Real World

When you check your mobile data usage, it might show 1.5 GB remaining. This means 1 GB + 0.5 GB. Or when you weigh vegetables, the digital scale might show 2.350 kg, which is 2 kg + 0.3 kg + 0.05 kg.

Key Vocabulary

Key Terms

DECIMAL: A number that includes a whole number part and a fractional part, separated by a decimal point | PLACE VALUE: The value of a digit based on its position in a number | TENTHS: The first digit after the decimal point, representing parts of ten (1/10) | HUNDREDTHS: The second digit after the decimal point, representing parts of a hundred (1/100) | EXPANDED FORM: A way of writing a number that shows the value of each digit.

What's Next

What to Learn Next

Great job learning expanded form! Next, you can explore 'Comparing and Ordering Decimals' or 'Adding and Subtracting Decimals'. Understanding expanded form will make these topics much easier, as you already know the value of each digit.