Q1.
For each number given below, write expressions for at least two different ways to obtain the number through button clicks. Think like Chitti and be creative. (a) 8300 (b) 40629 (c) 56354 (d) 66666 (e) 367813
Answer
The first way in each pair uses the digits of the number itself; the second trades one big button for ten smaller ones.
| Number | Way 1 | Way 2 |
|---|---|---|
| (a) 8300 | (8 × 1000) + (3 × 100) | (83 × 100) |
| (b) 40629 | (4 × 10000) + (6 × 100) + (2 × 10) + (9 × 1) | (40 × 1000) + (62 × 10) + (9 × 1) |
| (c) 56354 | (5 × 10000) + (6 × 1000) + (3 × 100) + (5 × 10) + (4 × 1) | (56 × 1000) + (35 × 10) + (4 × 1) |
| (d) 66666 | (6 × 10000) + (6 × 1000) + (6 × 100) + (6 × 10) + (6 × 1) | (66 × 1000) + (6 × 100) + (66 × 1) |
| (e) 367813 | (3 × 100000) + (6 × 10000) + (7 × 1000) + (8 × 100) + (1 × 10) + (3 × 1) | (36 × 10000) + (78 × 100) + (13 × 1) |
Check (b), Way 2: 40 × 1000 = 40,000
62 × 10 = 620
9 × 1 = 9
40,000 + 620 + 9 = 40,629 ✓
Check (e), Way 2: 36 × 10,000 = 3,60,000
78 × 100 = 7,800
13 × 1 = 13
3,60,000 + 7,800 + 13 = 3,67,813 ✓
62 × 10 = 620
9 × 1 = 9
40,000 + 620 + 9 = 40,629 ✓
Check (e), Way 2: 36 × 10,000 = 3,60,000
78 × 100 = 7,800
13 × 1 = 13
3,60,000 + 7,800 + 13 = 3,67,813 ✓
Why it happens: Because 1000 = 10 × 100 and 100 = 10 × 10, you can always split a big button into ten of the next smaller one. In (a), one +1000 press was traded for ten +100 presses: 8 thousands + 3 hundreds became 83 hundreds.
Try This: Write a third way for 8300, such as (5 × 1000) + (33 × 100) = 5000 + 3300 = 8300. How many clicks is that? 5 + 33 = 38.