Decimal Multiplication

Class 7 Maths · Chapter 12: Another Peek Beyond the Point · NCERT Ganita Prakash section P2 4.2

Learn

A pen costs ₹9.5. Five pens cost 9.5 + 9.5 + 9.5 + 9.5 + 9.5 = ₹47.5. As fractions: 95/10 × 5 = 475/10 = 47.5. A car going 12.5 km per litre covers 12.5 × 7.5 = 125/10 × 75/10 = 9375/100 = 93.75 km on 7.5 litres.

12.5 × 7.5 = 93.75

The rule: multiply the numbers without the points, then the product has as many decimal places as the two numbers together. 596 × 248 = 147808, so 5.96 × 24.8 has 2 + 1 = 3 places: 147.808. And 5.8 × 1.24: 58 × 124 = 7192, 3 places, so 7.192.

5.96 × 24.8 = 147.808

Why it works: decimals are fractions over 10, 100, 1000 …, and multiplying the denominators adds their zeros: 10 × 100 = 1000. Neel walks 0.827 km each way to school, so in a day 0.827 × 2 = 1.654 km, and in 6 days 9.924 km.

1.654 × 6 = 9.924

Bigger or smaller? 2.25 × 8 = 18 is bigger than both; 0.25 × 8 = 2 lies between; 0.25 × 0.8 = 0.2 is smaller than both. Just like fractions: multiplying by a number between 0 and 1 makes things smaller. And 56.50 × 2.250 is the same as 56.5 × 2.25: trailing zeros after the point change nothing.

0.25 × 0.8 = 0.2

Explore: less than 1?

1. Sort the products without working them out fully.

Remember

• Multiply without the points; the product's decimal places = the sum of both numbers' places.
• A factor between 0 and 1 makes the product smaller than the other number.

Quick check

18 × 12 = 216. What is 0.18 × 0.12?

1. 0.0216
2. 0.216
3. 2.16
4. 0.00216

Think about it

A shop buys notebooks at ₹23.6 each and sells them at ₹30. What is the profit on 50 books?

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.