A certain street has 1000 buildings. A sign-maker is contracted to number the houses from 1 to 1000. How many zeroes will he need?
Question
A certain street has 1000 buildings. A sign-maker is contracted to number the houses from 1 to 1000. How many zeroes will he need?
Solution
To solve this problem, we need to consider how many times the number '0' appears in each set of numbers:
- From 1 to 9, there are no zeroes.
- From 10 to 99, '0' appears 10 times in the units place (10, 20, 30, ..., 90) and 10 times in the tens place (10, 20, ..., 90). So, a total of 20 times.
- From 100 to 999, '0' appears:
- 100 times in the units place (100, 110, 120, ..., 990)
- 100 times in the tens place (100, 101, ..., 199, 200, 201, ..., 299, ..., 900, 901, ..., 999)
- 10 times in the hundreds place (100, 200, ..., 1000) So, a total of 210 times.
- In 1000, '0' appears 3 times.
Adding these all up, the sign-maker will need 0 (from step 1) + 20 (from step 2) + 210 (from step 3) + 3 (from step 4) = 233 zeroes.
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