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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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    How about "$\tau = 2.745 \times 10^2$ in base $16$" (or "τ = 2.745e2 in base 16", whichever you prefer)?2011-06-05
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    what's a bit ugly is that you're still using base 10 to denote the base you're using. Maybe, in a way, it's more natural to denote your base by the highest number below the radix, instead of the radix itself, so you'd have base 9 or base F instead of base 10 or base 16 in 'metabase' 10.2011-06-05
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    @gfes I think your (base-1) notation has some appeal, but using 10 as the "metabase" seems to be the only way I've ever seen it done, and seems to be universally understood. "Base F" immediately makes one think of hexadecimal, but I think if you wrote "base 9" it would be confusing!2011-06-05
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    True. Although when working in base 10, probably anyone would omit the base 9 / base 10 altogether anyway. Also, I thought of a neater, but less practical way, namely writing the alternative expansion for the radix. I.e. 9.9999999999 etc. or F.FFFFFFFFF etc.2011-06-05
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    @gfes The alternate expansion is quite clever. It would work especially well with an overbar to indicate a the repeating fractional part.2011-06-05
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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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