To find how many times the digit 7 appears in the numbers from 103 to 200, we can break it down into steps.
### Step 1: Count occurrences of 7 in the range 103 to 199
First, we will check the numbers from 103 to 199 (since 200 does not contain the digit 7).
### Step 2: Count occurrences in the tens and units place
We will analyze the occurrences of the digit 7 in both the tens and units places separately.
#### Counting occurrences of 7 in the units place:
- The units place can have the digit 7 in the following numbers:
- 107, 117, 127, 137, 147, 157, 167, 177, 187, 197
- This gives us a total of **10 occurrences** of the digit 7 in the units place.
#### Counting occurrences of 7 in the tens place:
- The tens place can have the digit 7 in the following numbers:
- 170, 171, 172, 173, 174, 175, 176, 177, 178, 179
- This gives us a total of **10 occurrences** of the digit 7 in the tens place.
### Step 3: Adjust for double counting
In the previous step, we counted the number 177 twice (once for the units place and once for the tens place). Therefore, we need to subtract 1 from the total count.
### Step 4: Calculate the total occurrences
- Total occurrences = Occurrences in units place + Occurrences in tens place - Double counted occurrences
- Total occurrences = 10 (units) + 10 (tens) - 1 (double count) = 19
### Step 5: Count occurrences in the number 200
Since 200 does not contain the digit 7, it does not contribute to our count.
### Final Count
Thus, the total number of times the digit 7 appears in the numbers from 103 to 200 is **19**.
### Answer
The answer is **19**.
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