Introduction to Decimals

Decimals are a way of representing numbers that are not whole. They help us express parts of a whole, and they are especially useful in measurements, money, and calculations involving fractions.

A decimal number has two parts:

• The whole number part (on the left side of the decimal point),
• The fractional part (on the right side of the decimal point).

Example: In the number 4.75: 4 is the whole number part and 75 is the fractional part.

1. Understanding Decimal Numbers

Place Value in Decimals

Each digit in a decimal number has a place value, depending on its position.

Digit	Place Value Name	Place Value
4	Tens	40
5	Units	5
3	Tenths	0.3
2	Hundredths	0.02
6	Thousandths	0.006

Reading Decimal Numbers

• 0.5 is read as "zero point five" or "five-tenths".
• 2.75 is read as "two point seven five".

2. Representing Decimals

Using Place Value Charts

Tens	Ones	.	Tenths	Hundredths
1	4	.	2	3

Number: 14.23

Using Number Line

Decimals can be shown on a number line. Between 0 and 1, divide into ten equal parts.

3. Comparing Decimals

Compare whole parts first, then tenths, hundredths, etc.

Example: Compare 3.45 and 3.457 → 3.457 is greater.

4. Converting Fractions into Decimals

• 1/2 = 0.5
• 3/4 = 0.75
• 5/10 = 0.5

5. Converting Decimals into Fractions

• 0.25 = 25/100 = 1/4
• 0.5 = 5/10 = 1/2

6. Addition of Decimals

  3.25
+ 1.75
------
  5.00
    

7. Subtraction of Decimals

  5.00
- 2.75
------
  2.25
    

8. Multiplication of Decimals

Multiplying by 10, 100, 1000: Shift decimal point to the right.

• 2.5 × 10 = 25
• 2.5 × 100 = 250

Multiplying Two Decimals

Example: 1.2 × 3.4 = 4.08

9. Division of Decimals

Dividing by 10, 100, 1000: Shift decimal point to the left.

• 25 ÷ 10 = 2.5
• 25 ÷ 100 = 0.25

Dividing by Decimal: Multiply both numbers to remove decimal in divisor. Example: 2.5 ÷ 0.5 = 5

10. Word Problems on Decimals

Example: 1 liter of milk costs Rs. 42.50. What is the cost of 1.5 liters?

Cost = 42.50 × 1.5 = Rs. 63.75

11. Use of Decimals in Daily Life

• Shopping: Rs. 199.99
• Cooking: 0.5 teaspoon salt
• Travel: Fuel efficiency, ticket cost
• Medicine: 5.5 ml dosage

Key Points to Remember

• Tenths = 1/10 = 0.1
• Hundredths = 1/100 = 0.01
• Align decimal points in addition/subtraction
• Consider place values in comparison

Practice Problems

1. Convert into decimals: 3/10, 17/100
2. Write as fractions: 0.6, 0.08
3. Compare: 0.7 ___ 0.65
4. Add: 2.35 + 1.25
5. Multiply: 3.2 × 4
6. Word Problem: 1 kg sugar costs Rs. 45.60. Find cost of 2.5 kg.

Conclusion

Decimals are essential for handling non-whole quantities. With clear understanding and practice, decimals become easy and practical to use in real-life situations.