## RonrickDaano 3 years ago Given that 2.004<log10101<2.005, how many digits are there in the decimal representation of 101101? Clarification: The decimal representation of 210 is 210=1024, which has 4 digits.

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10101 in binary? then 210 shouldn't be binary....

2. jishan

( 101101)base2=( 45)decimal binary no always power of 2 therefore 2power 6= 64 hence 6 digit req..

3. shubham.bagrecha

brilliant!

4. shubham.bagrecha

it is 101^101

5. shubham.bagrecha

@ParthKohli

6. shubham.bagrecha

help!

7. ParthKohli

Well, find out \(\log_{10} 101^{101}\)

8. shubham.bagrecha

then

9. ParthKohli

That's it.

10. shubham.bagrecha

that is the no. of digits?

11. ParthKohli

Yes

12. shubham.bagrecha

how log can help calculate no. of digits?

13. ParthKohli

Yes, it does. Try it!

14. shubham.bagrecha

202 is incorrect

15. ParthKohli

You also have to consider the assumptions given in your question.

16. shubham.bagrecha

what else is given?

17. ParthKohli

Actually, you have to find \(1 + \log_{10} 101^{101}\). Don't write in the answer, let me check first.

18. shubham.bagrecha

ok

19. ParthKohli

You can do something else while I check. Thanks :-)

20. shubham.bagrecha

ok

21. ParthKohli

203.

22. ParthKohli

And so I was correct :-)

23. shubham.bagrecha

24. ParthKohli

Because the number of digits in \(100\) is not \(\log_{10} 100\), but it's \(1+\log_{10}100\)

25. shubham.bagrecha

ok thanks

26. shubham.bagrecha

can it be used for counting digits in any expansion?

27. ParthKohli

Expansion? You mean number base?

28. shubham.bagrecha

like this type of question

29. ParthKohli

Yes.

30. shubham.bagrecha

ok thanks