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Is there a standard or common way to write scientific notation in different bases that doesn't require repeating the base in both the coefficient and the exponent base?

For example, this notation is correct, but is quite verbose:

  • Implicit base 10: $100 \cdot \tau = 6.283 \times 10^2$
  • Explicit base 10: $100 \cdot \tau = 6.283_{10} \times 10_{10}^2$
  • Explicit base 16: $100 \cdot \tau = 2.745_{16} \times 10_{16}^2$

Most calculators & programming languages shorten this to an "exponent" notation such as:

6.283e2 

Some rare ones even support a base, such as:

16#2.745#e2# 

Unfortunately, these are not very nice notations outside of specific domains.

Ideally, I'm looking for an operator notation that concisely does the function:

  • $f(coefficient_{b},exponent) = coefficient_{b} \times b^{exponent}$

If there is no such standard or common notation, I'd be happy to hear any suggestions.

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    I agree. Using an overbar is a great idea. It could actually make this notation feasible.2011-06-05

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Unfortunately, $2.546_{16}\times 10_{16}^{23}$ is cumbersome, and it isn't immediately clear if the exponent is being written in base $10$ or base $16$, and $2.546_{16}\times 16^{23}$ has a strange mixing of base $10$ and base $16$ elements. For programming things, there are explicit prefixes you can put on a number to denote whether it is base $2,8,10$ or $16$, but that isn't general, and it still doesn't really address any of the previous problems.

Maybe a notation like $(2.546\times b^{23})_{16}$ would work to indicate that everything is supposed to be taken base $16$, with $b$ being implicit for the base (as writing either 10 or the base 10 expression of the base is awkward). However, I'm not fully enamored with this notation either.

What is your application of this? In what circumstances is some sort of scientific notation required but base $10$ is undesirable?

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    Um, one possibility is also to use the shift operators _a la_ C/C++. So $(2.546 \ll 23)_{16}$?2011-07-05