Solve 6.6710^-11*100*7.1210^18/100+6.410^-3

$$\frac{ 6.67 { 10 }^{ -11 } \times 100 \times 7.12 { 10 }^{ 18 } }{ 100+6.4 { 10 }^{ -3 } }$$

Evaluate

$$\frac{3710187500000}{7813}\approx 474873608.089082299$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -11 and 18 to get 7.

$$\frac{6.67\times 10^{7}\times 100\times 7.12}{100+6.4\times 10^{-3}}$$

Calculate 10 to the power of 7 and get 10000000.

$$\frac{6.67\times 10000000\times 100\times 7.12}{100+6.4\times 10^{-3}}$$

Multiply 6.67 and 10000000 to get 66700000.

$$\frac{66700000\times 100\times 7.12}{100+6.4\times 10^{-3}}$$

Multiply 66700000 and 100 to get 6670000000.

$$\frac{6670000000\times 7.12}{100+6.4\times 10^{-3}}$$

Multiply 6670000000 and 7.12 to get 47490400000.

$$\frac{47490400000}{100+6.4\times 10^{-3}}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{47490400000}{100+6.4\times \frac{1}{1000}}$$

Multiply 6.4 and \frac{1}{1000} to get \frac{4}{625}.

$$\frac{47490400000}{100+\frac{4}{625}}$$

Add 100 and \frac{4}{625} to get \frac{62504}{625}.

$$\frac{47490400000}{\frac{62504}{625}}$$

Divide 47490400000 by \frac{62504}{625} by multiplying 47490400000 by the reciprocal of \frac{62504}{625}.

$$47490400000\times \frac{625}{62504}$$

Multiply 47490400000 and \frac{625}{62504} to get \frac{3710187500000}{7813}.

$$\frac{3710187500000}{7813}$$

Factor

$$\frac{23 \cdot 29 \cdot 89 \cdot 2 ^ {5} \cdot 5 ^ {9}}{13 \cdot 601} = 474873608\frac{696}{7813} = 474873608.0890823$$