Mathematics

# What proportion of the first 10,000 natural numbers contain a 3

#### Banaszek168

4 years ago

In the first 10 -> 10 - 9 = 1 (contain a 3).
In the first 100 -> 100 - 9 * 9 = 19 (contain a 3).
In the first 10^n -> 10^n - 9^n  (contain a 3).

$So for 10^4 -> 10^4 - 9^4 = 10.000 - 6.561 = 3.439$

The answer is 3.439 numbers contain a 3 in the first 10.000