Question

We write the integers from 1 to 150 inclusive. What is the total number of digits that must be written?

Answer 1

342

Explanation:

First, there are 9 one-digit numbers, so 9x1=9. Next, there are 90 two-digit numbers, so 90x2=180. There are 51 numbers between 100-150, so 51x3=153. Now, we do 9+180+153=342 digits.

Answer 2

Explanation:

Solution

Break the numbers down by the number of digits in that sequence.

Number of digits 1 to 9 = 9

Number of digits from 10 to 99

There are 90 numbers between 10 and 99

Each has 2 digits

The total number of digits is 180

Number of digits from 100 to 150

There are 51 numbers between 100 and 150

Each has 3 digits

The total number of digits = 3*51 153 Add

Total number of digits = 342

Answer: 342