The Decimal Number System

• Decimals are used to write numbers that have a whole part and a fractional part (less than 1).

• The decimal point (.) separates the whole part and the fractional part.

• If the denominator is 10 → place the decimal after 1 digit from the right.

• If the denominator is 100 → place it after 2 digits from the right.

• If the denominator is 1000 → after 3 digits from the right. 

1. Writing Decimal Numbers:

• If there’s no digit before the decimal point, write 0.
• Example: Write 0.72 instead of .72.
• Example: 2.4 means 2 + 0.4.

2. Effect of Zeros After the Decimal:

• Zeros after the decimal point don’t change the number.
• Example: 3.5 = 3.50 = 3.500.

3. Reading Decimal Numbers:

• Read the whole number part, then say “point”, and read the fractional part.
• Example: 8.5 is read as “eight point five”.

4. Place Value System:

• Left of the decimal: Whole numbers (ones, tens, hundreds).
• Right of the decimal: Fractions (tenths, hundredths, thousandths).
• Each place to the right is 10 times smaller than the previous one.

• Money: ₹1.50 → 1 rupee + 50 paise.

• Measurement: 2.5 m → 2 metres + 50 centimetres.

• Weight: 1.25 kg → 1 kg + 250 g.

• Decimal point shows where the whole part ends and the fractional part starts.

• Fractions with denominators 10, 100, 1000… are decimal fractions.

• Place value determines where the decimal point is placed.

• We use decimals daily in money, measurement, and weight.