find the number of 3digit number in the base 7 system
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The first 3 digit number which will have exactly 3 digits when expressed in both base 7 and base 13 =169.
The last 3 digit number which will have exactly 3 digits when expressed in both base 7 and base 13 = 342.
The required number of decimal numbers that have exactly 3 digits when expressed in both base 7 and base 13 = 342 - 168 = 174.
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Answer:
Total number of three-digit numbers in base 7 system = 6*7*7 = 294. In base 10 system, three -digit numbers vary from 100 to 999.
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