What is a Decimal?
A decimal is a way of writing numbers that are not whole — parts of a whole using a decimal point (.).
- The part to the left of the decimal point is the whole number.
- The part to the right of the decimal point is the fractional part.
Example: 27.35
- Whole part: 27
- Fractional part: 0.35 (35 hundredths)
Place Value in Decimals
| Thousands | Hundreds | Tens | Ones | . | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|---|---|
| 1,000 | 100 | 10 | 1 | . | 1/10 | 1/100 | 1/1000 |
Example: Write the place value of each digit in 24.356
| Digit | Place | Value |
|---|---|---|
| 2 | Tens | 20 |
| 4 | Ones | 4 |
| 3 | Tenths | 3/10 = 0.3 |
| 5 | Hundredths | 5/100 = 0.05 |
| 6 | Thousandths | 6/1000 = 0.006 |
Reading and Writing Decimals
Reading: Say the whole part, "point", then each decimal digit.
- 5.3 → "five point three"
- 12.07 → "twelve point zero seven"
Expanded form: 27.35 = 20 + 7 + 3/10 + 5/100
Decimals as Fractions
| Decimal | Fraction |
|---|---|
| 0.1 | 1/10 |
| 0.01 | 1/100 |
| 0.001 | 1/1000 |
| 0.5 | 5/10 = 1/2 |
| 0.25 | 25/100 = 1/4 |
| 0.75 | 75/100 = 3/4 |
| 1.3 | 13/10 = 1 3/10 |
Converting fraction to decimal:
- 3/4: divide 3 by 4 → 0.75
- 2/5: multiply to get denominator 10: 2/5 = 4/10 = 0.4
Decimals on a Number Line
Between 0 and 1, divide into 10 equal parts:
Between 1 and 2, the same pattern: 1.1, 1.2, 1.3, …
Comparing Decimals
Step 1: Compare whole number parts. Larger whole part → greater number.
Step 2: If whole parts are equal, compare tenths.
Step 3: If tenths are equal, compare hundredths. Continue.
Tip: Add trailing zeros to make the same number of decimal places, then compare.
Example: Compare 4.6 and 4.57.
- Write 4.60 and 4.57
- Whole parts: 4 = 4
- Tenths: 6 > 5
- So 4.6 > 4.57
Example: Arrange in ascending order: 2.1, 2.01, 2.001, 2.10
- Write as: 2.100, 2.010, 2.001, 2.100
- Ascending: 2.001, 2.01, 2.1, 2.10 (note 2.1 = 2.10)
Addition of Decimals
1. Write numbers with decimal points aligned (one below the other). 2. Add trailing zeros if needed. 3. Add digit by digit from right to left, carrying if necessary. 4. Place the decimal point in the answer directly below the others.
Example: 3.5 + 2.47
Subtraction of Decimals
Same as addition — align decimal points, add zeros, subtract.
Example: 7.3 − 4.56
Uses of Decimals in Daily Life
- Money: ₹15.75 means 15 rupees and 75 paise
- Weight: 2.5 kg means 2 kilograms 500 grams
- Length: 1.35 m means 1 metre 35 centimetres
- Temperature: 36.8°C (body temperature)
Key Vocabulary
| Term | Meaning |
|---|---|
| Decimal point | The dot separating whole and fractional parts |
| Tenths | First digit after decimal point (÷10) |
| Hundredths | Second digit after decimal point (÷100) |
| Thousandths | Third digit after decimal point (÷1000) |
| Like decimals | Same number of decimal places |
| Unlike decimals | Different number of decimal places |
Exam Tips
- Always align decimal points before adding or subtracting.
- Trailing zeros don't change the value: 3.5 = 3.50 = 3.500.
- Convert fractions to decimals: 3/5 = 6/10 = 0.6.
- 1 paise = 0.01 rupee (100 paise = 1 rupee).
- Place value: digit 5 in 4.537 → 5 is in tenths place → value is 5/10 = 0.5.
- Compare by writing equal decimal places: don't compare 0.7 and 0.70 separately — they're equal.