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How do I calculate $$\frac{1}{{\frac{1}{7 \times 10^7}- \frac{8\times10^{17}\times 3.1\times 10^7}{6.7 \times 10^{-11}\times \left(1.9 \times 10^{27}\right)^2} }}\tag{1}$$

To arbitrary precision?

I put it into Wolfram Alpha and it simply returns the value $7\times 10^7$

Remark: I am new here and this is my first question since this stack exchange site is called 'Mathematica and Wolfram Language' I assumed questions about Wolfram Alpha were allowed. If it turns out that this stack exchange site is only for Mathematica then I have that downloaded also, but I am a complete beginner so I'm not sure which command gives arbitrary precision.

Could someone please explain how to get a precise value of $(1)$ with Mathematica?

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  • $\begingroup$ It would be nice if you could give the input expression as type into WA so others can just copy it and don't have to translate it from the latex input. $\endgroup$
    – Max1
    May 1, 2020 at 9:01

1 Answer 1

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1/(1/(7*10^7) - (8*10^17*31*10^6)/(67*10^-12*(19*10^26)^2))
(*    2116362500000000000000/30233749999783    *)

% // N
(*    7.*10^7    *)

N[2116362500000000000000/30233749999783, 100]
(*    7.000000000050241865465279777890799709324920115332153889776394836700094354142768279649364723750243094*10^7    *)
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