Solve 8*10^-8+15*10^-9/9*10^-4+10^-3

$$\frac { 8 \times 10 ^ { - 8 } + 15 \times 10 ^ { - 9 } } { 9 \times 10 ^ { - 4 } + 10 ^ { - 3 } }$$

Evaluate

$$\frac{1}{20000}=0.00005$$

Solution Steps

Calculate 10 to the power of -8 and get \frac{1}{100000000}.

$$\frac{8\times \frac{1}{100000000}+15\times 10^{-9}}{9\times 10^{-4}+10^{-3}}$$

Multiply 8 and \frac{1}{100000000} to get \frac{1}{12500000}.

$$\frac{\frac{1}{12500000}+15\times 10^{-9}}{9\times 10^{-4}+10^{-3}}$$

Calculate 10 to the power of -9 and get \frac{1}{1000000000}.

$$\frac{\frac{1}{12500000}+15\times \frac{1}{1000000000}}{9\times 10^{-4}+10^{-3}}$$

Multiply 15 and \frac{1}{1000000000} to get \frac{3}{200000000}.

$$\frac{\frac{1}{12500000}+\frac{3}{200000000}}{9\times 10^{-4}+10^{-3}}$$

Add \frac{1}{12500000} and \frac{3}{200000000} to get \frac{19}{200000000}.

$$\frac{\frac{19}{200000000}}{9\times 10^{-4}+10^{-3}}$$

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$\frac{\frac{19}{200000000}}{9\times \frac{1}{10000}+10^{-3}}$$

Multiply 9 and \frac{1}{10000} to get \frac{9}{10000}.

$$\frac{\frac{19}{200000000}}{\frac{9}{10000}+10^{-3}}$$

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

$$\frac{\frac{19}{200000000}}{\frac{9}{10000}+\frac{1}{1000}}$$

Add \frac{9}{10000} and \frac{1}{1000} to get \frac{19}{10000}.

$$\frac{\frac{19}{200000000}}{\frac{19}{10000}}$$

Divide \frac{19}{200000000} by \frac{19}{10000} by multiplying \frac{19}{200000000} by the reciprocal of \frac{19}{10000}.

$$\frac{19}{200000000}\times \frac{10000}{19}$$

Multiply \frac{19}{200000000} and \frac{10000}{19} to get \frac{1}{20000}.

$$\frac{1}{20000}$$

Factor

$$\frac{1}{2 ^ {5} \cdot 5 ^ {4}} = 5 \times 10^{-5}$$