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When 30(10) = 1E(16) and 100(10) = 1a(64), what is the result of 199(10) = x(100)?

a51
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    What symbol do you use to represent $99$ in base $100$? – rogerl Jul 11 '19 at 14:08
  • $36_{10}=1E_{16}$ ??? –  Jul 11 '19 at 14:22
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    Welcome to stackexchange. Please provide some more details and background to your question and show your own efforts. Otherwise people may not be able to (or want to) help you. – Mars Plastic Jul 11 '19 at 14:22
  • Mars Plastic: I'm not sure what details would that be, could you be more specific please? – a51 Jul 11 '19 at 14:25
  • Yves Daoust: Thank you, I made a mistake. It should be 30(10) = 1E(16). – a51 Jul 11 '19 at 14:29
  • You do not need symbols. You can also write down the number in vector form , for example $[3,7,91,22]$ for $3\cdot 100^3+7\cdot 100^2+91\cdot 100+22$. PARI/GP for example uses this possibility. – Peter May 05 '22 at 20:08

2 Answers2

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To write numbers in base $100$ you need $100$ different "digits", starting with $0$ and ending with whatever represents $99$. I would use the (base $10$) numbers $0, \ldots, 99$ for the digits, so, for example the number $12345$ (in base $10$) is $(1)(23)(45)$ in base $100$. You just group the ordinary digits in pairs, starting from the right.

So $199$ would be $(1)(99)$.

Ethan Bolker
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    There is a precedent for this in ordinary life. Our timekeeping system of hours, minutes, and seconds is a base-sixty system inherited from the Babylonians. But we write the individual place values in that system (for example, the number of minutes) using two decimal digits. – David K Jul 11 '19 at 14:14
  • David K: But then there's also precedent for using letters as a representation of numbers when writing numbers in hexadecimal... – a51 Jul 11 '19 at 14:16
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I think I'm the only one that does this, but what I do is use $[\dots ,cc, bb, aa]$ notation. For example

$12345_{10} = [1,23,45]_{100}$.

Steven Alexis Gregory
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  • You are not. The author of PARI/GP does this as well , it would also be my way to write it down, but that might be a matter of taste. I wonder why this answer has a much worse score than the above one although it is an utterly equivalent method , just a little bit different written down (+1) – Peter May 06 '22 at 09:28