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RonrickDaano

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.

  • one year ago
  • one year ago

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

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

    • one year ago
  3. shubham.bagrecha
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    brilliant!

    • one year ago
  4. shubham.bagrecha
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    it is 101^101

    • one year ago
  5. shubham.bagrecha
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    @ParthKohli

    • one year ago
  6. shubham.bagrecha
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    help!

    • one year ago
  7. ParthKohli
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    Well, find out \(\log_{10} 101^{101}\)

    • one year ago
  8. shubham.bagrecha
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    then

    • one year ago
  9. ParthKohli
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    That's it.

    • one year ago
  10. shubham.bagrecha
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    that is the no. of digits?

    • one year ago
  11. ParthKohli
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    Yes

    • one year ago
  12. shubham.bagrecha
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    how log can help calculate no. of digits?

    • one year ago
  13. ParthKohli
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    Yes, it does. Try it!

    • one year ago
  14. shubham.bagrecha
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    202 is incorrect

    • one year ago
  15. ParthKohli
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    You also have to consider the assumptions given in your question.

    • one year ago
  16. shubham.bagrecha
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    what else is given?

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

    • one year ago
  18. shubham.bagrecha
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    ok

    • one year ago
  19. ParthKohli
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    You can do something else while I check. Thanks :-)

    • one year ago
  20. shubham.bagrecha
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    ok

    • one year ago
  21. ParthKohli
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    203.

    • one year ago
  22. ParthKohli
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    And so I was correct :-)

    • one year ago
  23. shubham.bagrecha
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    why add 1?

    • one year ago
  24. ParthKohli
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    Because the number of digits in \(100\) is not \(\log_{10} 100\), but it's \(1+\log_{10}100\)

    • one year ago
  25. shubham.bagrecha
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    ok thanks

    • one year ago
  26. shubham.bagrecha
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    can it be used for counting digits in any expansion?

    • one year ago
  27. ParthKohli
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    Expansion? You mean number base?

    • one year ago
  28. shubham.bagrecha
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    like this type of question

    • one year ago
  29. ParthKohli
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    Yes.

    • one year ago
  30. shubham.bagrecha
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    ok thanks

    • one year ago
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