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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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  1. Shadowys
    • 3 years ago
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    10101 in binary? then 210 shouldn't be binary....

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

  3. shubham.bagrecha
    • 3 years ago
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    brilliant!

  4. shubham.bagrecha
    • 3 years ago
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    it is 101^101

  5. shubham.bagrecha
    • 3 years ago
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    @ParthKohli

  6. shubham.bagrecha
    • 3 years ago
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    help!

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

  8. shubham.bagrecha
    • 3 years ago
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    then

  9. ParthKohli
    • 3 years ago
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    That's it.

  10. shubham.bagrecha
    • 3 years ago
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    that is the no. of digits?

  11. ParthKohli
    • 3 years ago
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    Yes

  12. shubham.bagrecha
    • 3 years ago
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    how log can help calculate no. of digits?

  13. ParthKohli
    • 3 years ago
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    Yes, it does. Try it!

  14. shubham.bagrecha
    • 3 years ago
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    202 is incorrect

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

  16. shubham.bagrecha
    • 3 years ago
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    what else is given?

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

  18. shubham.bagrecha
    • 3 years ago
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    ok

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

  20. shubham.bagrecha
    • 3 years ago
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    ok

  21. ParthKohli
    • 3 years ago
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    203.

  22. ParthKohli
    • 3 years ago
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    And so I was correct :-)

  23. shubham.bagrecha
    • 3 years ago
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    why add 1?

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

  25. shubham.bagrecha
    • 3 years ago
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    ok thanks

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

  27. ParthKohli
    • 3 years ago
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    Expansion? You mean number base?

  28. shubham.bagrecha
    • 3 years ago
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    like this type of question

  29. ParthKohli
    • 3 years ago
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    Yes.

  30. shubham.bagrecha
    • 3 years ago
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    ok thanks

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