Explanation of Question no. 12 is Number system 1 questions PDF not clear. please explain this in detail and step wise so I can understand it.

Hi Saajan, please post the question here so we can try to break it down and explain it for you. keep practising.

If N= 123456789101112......9998999910000 and the number of digits in N is P, find the number of digits P has, if it is represented in base 7.

Hi Sajaan, as per the question N is a clear concatenation so after connecting numbers end to end from 1 to 10000 p=9+180+2700+36000+5=38894 Now we need digits in base 7 Digits=⌊log7​(38894)⌋+1 Now check powers of 7: (7^5 = 16807) clearly 7^6 exceeds 38894 so the number of digits would be 6.