Introduction to Decimals
A decimal is a way of writing numbers that are not whole. The decimal point (.) separates the whole number part from the fractional part. Decimals are closely related to fractions and are used everywhere — in money, measurements, and more.
For example, ₹5.50 means 5 rupees and 50 paise. The number after the decimal point represents a part of a whole.
What is Introduction to Decimals - Class 4 Maths (Decimals)?
A decimal number has two parts separated by a decimal point:
- The digits to the left of the decimal point form the whole number part.
- The digits to the right of the decimal point form the decimal (fractional) part.
Example: In 3.7, the whole number part is 3 and the decimal part is 7 (which means 7 tenths).
| Ones | Decimal Point | Tenths |
|---|---|---|
| 3 | . | 7 |
So 3.7 = 3 + 7/10 = 3 and 7 tenths.
Types and Properties
Relationship Between Fractions and Decimals:
| Fraction | Decimal | In Words |
|---|---|---|
| 1/10 | 0.1 | One tenth |
| 3/10 | 0.3 | Three tenths |
| 1/2 | 0.5 | Five tenths (half) |
| 1/4 | 0.25 | Twenty-five hundredths |
| 3/4 | 0.75 | Seventy-five hundredths |
Solved Examples
Example 1: Example 1: Identify Parts of a Decimal
Problem: In the number 5.3, identify the whole number part and the decimal part.
Solution:
Step 1: The digit before the decimal point = 5 (whole number part).
Step 2: The digit after the decimal point = 3 (decimal part = 3 tenths).
Answer: Whole part = 5, Decimal part = 3 tenths (0.3). So 5.3 = 5 + 3/10.
Example 2: Example 2: Write as a Decimal
Problem: Write 7/10 as a decimal.
Solution:
Step 1: 7/10 means 7 tenths.
Step 2: In decimal form, tenths go in the first place after the decimal point.
Answer: 7/10 = 0.7
Example 3: Example 3: Write as a Fraction
Problem: Write 0.4 as a fraction.
Solution:
Step 1: 0.4 = 4 tenths = 4/10.
Step 2: Simplify: 4/10 = 2/5.
Answer: 0.4 = 4/10 = 2/5
Example 4: Example 4: Read a Decimal
Problem: How do you read 12.6?
Solution:
Step 1: Whole part = 12, Decimal part = 6 tenths.
Answer: 12.6 is read as "twelve point six" or "twelve and six tenths".
Example 5: Example 5: Place Value in Decimals
Problem: What is the place value of 8 in 3.8?
Solution:
Step 1: 8 is in the tenths place (first digit after the decimal point).
Step 2: Place value = 8 × 1/10 = 8/10 = 0.8.
Answer: The place value of 8 is 8 tenths (0.8).
Example 6: Example 6: Write in Expanded Form
Problem: Write 4.9 in expanded form.
Solution:
Step 1: 4.9 = 4 + 0.9
Step 2: = 4 ones + 9 tenths
Step 3: = 4 + 9/10
Answer: 4.9 = 4 + 9/10
Example 7: Example 7: Decimal on a Number Line
Problem: Mark 0.6 on a number line between 0 and 1.
Solution:
Step 1: Divide the line from 0 to 1 into 10 equal parts.
Step 2: Each part = 0.1.
Step 3: Count 6 parts from 0.
0 — 0.1 — 0.2 — 0.3 — 0.4 — 0.5 — 0.6 — 0.7 — 0.8 — 0.9 — 1
Answer: 0.6 is at the 6th mark.
Example 8: Example 8: Money as Decimals
Problem: Rahul has 8 rupees and 50 paise. Write this amount using a decimal.
Solution:
Step 1: 50 paise = 50/100 rupees = 0.50 rupees.
Step 2: Total = 8 + 0.50 = 8.50.
Answer: ₹8.50
Example 9: Example 9: Word Problem
Problem: Aditi ran 2.5 km and Priya ran 3.2 km. Who ran more? By how much?
Solution:
Step 1: Compare: 3.2 > 2.5, so Priya ran more.
Step 2: Difference = 3.2 − 2.5 = 0.7 km.
Answer: Priya ran more, by 0.7 km.
Key Points to Remember
- A decimal point separates the whole number part from the fractional part.
- The first place after the decimal point is the tenths place.
- Decimals are another way to write fractions with denominators of 10, 100, etc.
- 0.1 = 1/10, 0.5 = 1/2, 0.25 = 1/4, 0.75 = 3/4.
- Money is written using decimals: ₹4.75 means 4 rupees and 75 paise.
- Decimals can be shown on a number line by dividing each whole unit into 10 equal parts.
Practice Problems
- Write the decimal for: 9 ones and 3 tenths.
- Write 6/10 as a decimal.
- What is the place value of 5 in 2.5?
- Write 0.8 as a fraction in simplest form.
- Kavi has Rs.12 and 25 paise. Write this as a decimal.
- Mark 0.3 and 0.8 on a number line from 0 to 1.
- Meera bought a pencil for Rs.3.50 and a rubber for Rs.1.25. How much did she spend in total?
Frequently Asked Questions
Q1. What is a decimal?
A decimal is a number that uses a decimal point to show a value between two whole numbers. The digits after the decimal point represent parts of a whole (tenths, hundredths, etc.).
Q2. What does the decimal point do?
The decimal point separates the whole number part (on the left) from the fractional part (on the right). In 5.3, the 5 is the whole part and 3 is 3 tenths.
Q3. How are decimals related to fractions?
Decimals are just another way of writing fractions with denominators of 10, 100, 1000, etc. For example, 0.7 = 7/10 and 0.25 = 25/100 = 1/4.
Q4. Is 0.5 the same as 1/2?
Yes. 0.5 = 5/10 = 1/2. Both represent exactly half.
Q5. How do you read a decimal number?
Read the whole part, say 'point', then read each digit after the decimal. For example, 4.7 is read as 'four point seven' or 'four and seven tenths'.
Q6. Where do we use decimals in daily life?
Decimals are used in money (Rs.25.75), measurements (3.5 km), temperature (37.2 degrees C), and weight (1.5 kg), among many other places.
Q7. Is 3.0 the same as 3?
Yes. 3.0 and 3 have the same value. The .0 means zero tenths, which does not change the value.
Q8. What comes after the tenths place?
The hundredths place. For example, in 2.35, the 3 is in the tenths place and the 5 is in the hundredths place.
Q9. Is introduction to decimals in the NCERT Class 4 syllabus?
Yes. Decimals are introduced in Class 4 NCERT Maths. Students learn about tenths, the decimal point, the relationship with fractions, and basic decimal operations.
