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Approximations


Yoruichi-san
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(Okay yes, this was inspired by an xkcd comic...;))

Find the most accurate approximation (for the the units given) that has 5 characters or less (not counting negative sign or decimal point) for the following:

1) Gravitational constant: 6.673x10^-11 (m^3/kg/s)

2) Avogadro's number: 6.022x10^23

3) Planck's constant: 6.026x10^-34 (m^2*kg/s)

4) Electron mass: 9.109x10^-31 (kg)

5) Boltzmann constant: 8.617x10^-5 (eV/K)

6) Permittivity of free space: 8.854x10^-12 (F/m)

7) Elementary charge: 1.602x10^-19 C

I.e. you could approximate a light-year as 99^8 (m).

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here's all my answers

7^-12

5^34

56^-19

38^-19

22^-3

24^-8

22^-14

and here's my pseudo-code that produced it.


for i in range(2,100):

result = i**int(math.log(value,i))

if result/value > 1:

	 result = result/value-1

else:

	 result = 1-result/value

if result < aprox:

	 aprox = result

	 index = i

	 exponent = int(math.log(value,i))

print(index,exponent)

Edited by phil1882
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