Q1.
We start writing numbers from 1, 2, 3 … and so on. There are nine 1-digit numbers. Find out how many numbers have two digits, three digits, four digits, and five digits.
Answer
Count from the first such number to the last one:
| Type | From – to | Working | How many |
|---|---|---|---|
| 1-digit | 1 – 9 | 9 − 1 + 1 | 9 |
| 2-digit | 10 – 99 | 99 − 10 + 1 | 90 |
| 3-digit | 100 – 999 | 999 − 100 + 1 | 900 |
| 4-digit | 1000 – 9999 | 9999 − 1000 + 1 | 9000 |
| 5-digit | 10,000 – 99,999 | 99,999 − 10,000 + 1 | 90,000 |
Why the count is 9, 90, 900, 9000 …: for a 3-digit number the first digit can be filled in 9 ways (1 to 9, not 0) and each of the other two digits in 10 ways (0 to 9). So 9 × 10 × 10 = 900. Every extra digit multiplies the count by 10.