Multiplying by 10, 100, 1,000

In your book, Maths Mela (Chapter 6, The Dairy Farm), we look for patterns when we multiply by 10, 100 and 1,000. When a number is multiplied by 10, it becomes 10 times bigger and each digit moves one place to the left: 10 × 45 = 450. In a place value table, the 4 moves from the tens to the hundreds, the 5 moves from the ones to the tens, and a 0 fills the ones place.

Multiplying by 100 moves each digit two places to the left: 8 × 100 = 800. Multiplying by 1,000 moves each digit three places to the left: 2 × 1,000 = 2 thousand = 2,000, and 20 × 1,000 = 20 thousand = 20,000.

What about 30 × 20? We can multiply numbers in any order, so think of 30 as 3 × 10 and 20 as 2 × 10. Then 30 × 20 = 3 × 10 × 2 × 10 = 3 × 2 × 10 × 10 = 6 × 100 = 600. The quick way: multiply 3 × 2 = 6, then write the two zeros, one from 30 and one from 20.

The same idea works for bigger numbers. 80 × 900: first 8 × 9 = 72, then write the three zeros (one from 80 and two from 900): 72,000. 5 × 7,000: first 5 × 7 = 35, then three zeros: 35,000. And 700 × 8: first 7 × 8 = 56, then two zeros: 5,600.