Solve 6.67*10^-11*5.97*10^24*0.3/(6371*10^3)^2

$$6.67 \times 10 ^ { - 11 } \times \frac { 5.97 \times 10 ^ { 24 } \times 0.3 } { ( 6371 \times 10 ^ { 3 } ) ^ { 2 } }$$

Evaluate

$$\frac{5193900}{1764767}\approx 2.94310807$$

Solution Steps

Calculate 10 to the power of -11 and get \frac{1}{100000000000}.

$$6.67\times \frac{1}{100000000000}\times \frac{5.97\times 10^{24}\times 0.3}{\left(6371\times 10^{3}\right)^{2}}$$

Multiply 6.67 and \frac{1}{100000000000} to get \frac{667}{10000000000000}.

$$\frac{667}{10000000000000}\times \frac{5.97\times 10^{24}\times 0.3}{\left(6371\times 10^{3}\right)^{2}}$$

Calculate 10 to the power of 24 and get 1000000000000000000000000.

$$\frac{667}{10000000000000}\times \frac{5.97\times 1000000000000000000000000\times 0.3}{\left(6371\times 10^{3}\right)^{2}}$$

Multiply 5.97 and 1000000000000000000000000 to get 5970000000000000000000000.

$$\frac{667}{10000000000000}\times \frac{5970000000000000000000000\times 0.3}{\left(6371\times 10^{3}\right)^{2}}$$

Multiply 5970000000000000000000000 and 0.3 to get 1791000000000000000000000.

$$\frac{667}{10000000000000}\times \frac{1791000000000000000000000}{\left(6371\times 10^{3}\right)^{2}}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{667}{10000000000000}\times \frac{1791000000000000000000000}{\left(6371\times 1000\right)^{2}}$$

Multiply 6371 and 1000 to get 6371000.

$$\frac{667}{10000000000000}\times \frac{1791000000000000000000000}{6371000^{2}}$$

Calculate 6371000 to the power of 2 and get 40589641000000.

$$\frac{667}{10000000000000}\times \frac{1791000000000000000000000}{40589641000000}$$

Reduce the fraction \frac{1791000000000000000000000}{40589641000000} to lowest terms by extracting and canceling out 1000000.

$$\frac{667}{10000000000000}\times \frac{1791000000000000000}{40589641}$$

Multiply \frac{667}{10000000000000} and \frac{1791000000000000000}{40589641} to get \frac{5193900}{1764767}.

$$\frac{5193900}{1764767}$$

Factor

$$\frac{29 \cdot 199 \cdot 2 ^ {2} \cdot 3 ^ {2} \cdot 5 ^ {2}}{23 \cdot 277 ^ {2}} = 2\frac{1664366}{1764767} = 2.9431080703571633$$