the floors 3 to 9 of a business building are being remodeled. the rooms will be numbered using all the whole numbers from 300 to 999. the front door of each room will be numbered with bronze digits. how many bronz numerals for the digit 3 will be needed to number these rooms?

Answer 1

To find out how many bronze numerals for the digit 3 will be needed, we need to count the number of occurrences of the digit 3 in the room numbers from 300 to 999.

In each hundred increment, the digit 3 will appear 10 times as the hundreds place (e.g., 300, 301, 302, ..., 399). Therefore, within the range of 300 to 999, the digit 3 will appear 7 times as the hundreds place (from 300 to 900).

In the remaining two places (tens and ones place) of the room number, each place can take on any of the ten digits (0-9). So, for each room number, there will be 10 choices for the tens and 10 choices for the ones, which gives us a total of 10 * 10 = 100 possible combinations in each hundred increment.

Since there are 7 hundred increments from 300 to 900, multiplying the number of combinations per increment (100) by the number of increments (7) gives us a total of 100 * 7 = 700 combinations within this range.

Therefore, the digit 3 will be needed 700 times as a bronze numeral to number the rooms from 300 to 999.