Let’s break it down:
Step 1: Look at Each Digit
Numbers have three places:
Hundreds place (like in 900)
Tens place (like in ninety
Ones place (like in 9, 19, 29)
We need to count all the 9s in these places!
Step 2: Count 9s in Each Place
Let’s count how many times 9 appears in each place from 1 to 999 (we will handle 1000 later).
Counting the Ones Place
Look at numbers like 9, 19, 29, 39, …, 99, 109, 119, 129, …, 199, …, 999
Each decade (group of ten numbers) has one number ending in 9.
Since there are 1000 numbers, we have 100 times where 9 appears in the ones place.
Counting the Tens Place
Look at numbers like 90, 91, 92, …, 99, 190, 191, 192, …, 199, and so on.
Again, in every 100 numbers, there are 10 numbers that have a 9 in the tens place.
There are 10 such groups, so we get 100 nines in the tens place.
Counting the Hundreds Place
Look at numbers like 900 to 999—every single one has a 9 in the hundreds place.
That’s 100 more nines!
Step 3: Add Them All Up!
100 (ones place)
100 (tens place)
100 (hundreds place)
Total: 300 nines!
Step 4: What About 1000?
The number 1000 doesn’t have any 9s, so we don’t count it.
Final Answer:
There are 300 times where we see the number 9 between 1 and 1000!
Mission Accomplished, Detective!