What is a Decimal Number?

S3-SA4-0070

Grade Level:

Class 6

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

Definition

What is it?

A decimal number is a number that has a whole part and a fractional part, separated by a decimal point. It helps us represent values that are not whole numbers, like prices or measurements, in a simple way.

Simple Example

Quick Example

Imagine you buy a packet of biscuits that costs Rupees 15 and 50 paise. You wouldn't say '15 rupees and 50 paise' every time. Instead, you'd write it as ₹15.50. Here, 15 is the whole part, and 50 is the fractional part, separated by the decimal point.

Worked Example

Step-by-Step

Let's convert the fraction 3/4 into a decimal number.

1. The fraction 3/4 means 3 divided by 4.
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2. Set up the division: 3 ÷ 4.
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3. Since 3 is smaller than 4, we put a 0 in the quotient and a decimal point after it. Then, we add a 0 after 3, making it 30.
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4. Now, divide 30 by 4. 4 goes into 30 seven times (4 x 7 = 28).
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5. Write 7 after the decimal point in the quotient. Subtract 28 from 30, which leaves 2.
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6. Add another 0 to the remainder 2, making it 20.
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7. Divide 20 by 4. 4 goes into 20 five times (4 x 5 = 20).
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8. Write 5 after the 7 in the quotient. Subtract 20 from 20, which leaves 0. The division is complete.

Answer: 3/4 as a decimal is 0.75.

Why It Matters

Decimal numbers are crucial for precision in many fields. Data scientists use them for accurate calculations, engineers for designing structures, and economists for financial analysis. Understanding decimals opens doors to careers in technology, finance, and scientific research.

Common Mistakes

MISTAKE: Reading 0.25 as 'zero point twenty-five' | CORRECTION: Read each digit after the decimal point separately, like 'zero point two five'.

MISTAKE: Confusing the place value of digits after the decimal (e.g., thinking 0.5 is the same as 0.05) | CORRECTION: Remember that the first digit after the decimal is tenths, the second is hundredths, and so on. 0.5 means 5 tenths, while 0.05 means 5 hundredths.

MISTAKE: Adding or subtracting decimals without aligning the decimal points | CORRECTION: Always align the decimal points vertically before adding or subtracting to ensure you are combining digits of the same place value.

Practice Questions

Try It Yourself

QUESTION: What is the decimal representation of one-half? | ANSWER: 0.5

QUESTION: A tailor uses 2.35 meters of cloth for a shirt and 1.5 meters for a pair of shorts. How much total cloth did he use? | ANSWER: 3.85 meters

QUESTION: If a 5 kg bag of rice costs ₹250.50, what is the cost of 1 kg of rice? (Round to two decimal places if needed) | ANSWER: ₹50.10

MCQ

Quick Quiz

Which of the following numbers is a decimal number?

123

45/7

8.9

None of the above

The Correct Answer Is:

Option C (8.90) is a decimal number because it has a whole part (8) and a fractional part (90) separated by a decimal point. Options A and B are a whole number and a fraction, respectively.

Real World Connection

In the Real World

When you check your mobile data usage, it's often shown as 1.25 GB or 0.7 GB remaining. This uses decimal numbers. Similarly, petrol prices at the pump, like ₹105.75 per liter, are always expressed using decimals to show precise values.

Key Vocabulary

Key Terms

DECIMAL POINT: The dot that separates the whole part from the fractional part of a decimal number | WHOLE PART: The digits to the left of the decimal point, representing whole units | FRACTIONAL PART: The digits to the right of the decimal point, representing parts of a whole | PLACE VALUE: The value of a digit based on its position in the number | TENTHS: The first place value after the decimal point (e.g., 0.1)

What's Next

What to Learn Next

Now that you understand what decimal numbers are, you're ready to learn how to compare and order them. This will help you decide which decimal number is bigger or smaller, a skill essential for understanding measurements and money better!