Recent experimental values for the universal gravitational constant, the mass and mean radius of Earth, and the standard gravitational acceleration are

Assuming a spherical Earth, these quantities are related by the expression \(g R_{\mathrm{E}}^{2}=G M_{\mathrm{E}}\).

(a) To how many significant digits is this relation satisfied using the recent data?

(b) Can you round off all the data to the same number of significant digits before multiplying and still satisfy this relation to that number of significant digits? If so, what numbers of significant digits work?

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G = 6.6738 x 10 m kg 11 My 5.9736 x 1024 kg RE 6.378 140 x 10 m g= 9.80665 m-s2