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To find how many times the digit '2' appears between 1 and 300, we can look at each digit place: hundreds, tens, and units. In the range from 1 to 299, '2' appears 100 times in the tens place (20-29), 30 times in the units place (2, 12, 22, ..., 292), and 100 times in the hundreds place (200-299). Therefore, in total, '2' appears 100 + 30 + 100 = 230 times. However, since we are only considering up to 300 (not including it), the final count remains 230.
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