Decimal Arithmetic Notes & Questions | Class 6 Mathematics | Drishti OS

Decimal Arithmetic

What you'll learn

Place-value rules for adding and subtracting decimals (align decimal points).
Multiplying decimals by whole numbers and by other decimals.
Dividing decimals by whole numbers and by powers of 10.
Estimating answers to catch place-value errors before they become habits.

Key concepts

Level 1 — Place value and basic operations

Verbal: Each digit in a decimal has a place — tenths (0.1), hundredths (0.01), thousandths (0.001).

Symbolic: 3.47 = 3 + 4/10 + 7/100 = 3 + 0.4 + 0.07.

Visual (place-value chart):

Ones	.	Tenths	Hundredths
3	.	4	7

Add/subtract: Line up decimal points vertically, then add column by column. 2.35 + 1.4 = 2.35 + 1.40 = 3.75.

Level 2 — Multiply, divide, and estimate

Multiply by whole number: 0.6 × 4 = 2.4 (6 tenths × 4 = 24 tenths).

Multiply decimals: Count total decimal places in factors; product has that many. 0.2 × 0.3 = 0.06 (1 + 1 = 2 places).

Divide by whole number: 4.8 ÷ 2 = 2.4. Divide by 10, 100: shift decimal left — 45.6 ÷ 10 = 4.56.

Operation	Quick check	Example
+/−	Decimal points aligned?	5.02 − 3.6 = 1.42
×	Count decimal places	1.25 × 0.4 = 0.500 = 0.5
÷ by 10ⁿ	Move point left n places	0.07 × 100 = 7

Worked example

A shopkeeper sells 2.5 kg rice at ₹38.50 per kg. Find the cost.

Step 1 — Multiply: 38.50 × 2.5
Step 2 — 3850 × 25 = 96250; three decimal places → 96.250
Step 3 — Cost = ₹96.25
Step 4 — Estimate: ~40 × 2.5 = 100 (close enough) ✓

Common mistakes

Mistake	Why it happens	Fix
Misaligned decimal points	Treating decimals as whole numbers	Always stack with points in one column
0.3 × 0.2 = 0.6	Multiplying without counting places	Product has 2 decimal places → 0.06
Moving decimal wrong way on ÷10	Confusion with ×10	Dividing by 10 → point moves left
Dropping trailing zeros early	1.50 seen as 1.5 only in wrong step	Keep place value until final answer

Quick check

Add 12.045 and 3.6.
Multiply 0.25 by 0.4.
Divide 56.7 by 10 and by 100.
Estimate then compute: 4.8 × 1.95.

Open the Practice tab for graded questions on Decimal Arithmetic.

Decimal Arithmetic