Solve 2*10^-7*20/0.05+0.1-2*10^-7*10/0.05

$$\frac { 2 \times 10 ^ { - 7 } \times 20 } { 0.05 + 0.1 } - \frac { 2 \times 10 ^ { - 7 } \times 10 } { 0.05 }$$

Evaluate

$$-\frac{1}{75000}\approx -0.000013333$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -7 and 1 to get -6.

$$\frac{2\times 10^{-7}\times 20}{0.05+0.1}-\frac{2\times 10^{-6}}{0.05}$$

Calculate 10 to the power of -7 and get \frac{1}{10000000}.

$$\frac{2\times \frac{1}{10000000}\times 20}{0.05+0.1}-\frac{2\times 10^{-6}}{0.05}$$

Multiply 2 and \frac{1}{10000000} to get \frac{1}{5000000}.

$$\frac{\frac{1}{5000000}\times 20}{0.05+0.1}-\frac{2\times 10^{-6}}{0.05}$$

Multiply \frac{1}{5000000} and 20 to get \frac{1}{250000}.

$$\frac{\frac{1}{250000}}{0.05+0.1}-\frac{2\times 10^{-6}}{0.05}$$

Add 0.05 and 0.1 to get 0.15.

$$\frac{\frac{1}{250000}}{0.15}-\frac{2\times 10^{-6}}{0.05}$$

Express \frac{\frac{1}{250000}}{0.15} as a single fraction.

$$\frac{1}{250000\times 0.15}-\frac{2\times 10^{-6}}{0.05}$$

Multiply 250000 and 0.15 to get 37500.

$$\frac{1}{37500}-\frac{2\times 10^{-6}}{0.05}$$

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$\frac{1}{37500}-\frac{2\times \frac{1}{1000000}}{0.05}$$

Multiply 2 and \frac{1}{1000000} to get \frac{1}{500000}.

$$\frac{1}{37500}-\frac{\frac{1}{500000}}{0.05}$$

Express \frac{\frac{1}{500000}}{0.05} as a single fraction.

$$\frac{1}{37500}-\frac{1}{500000\times 0.05}$$

Multiply 500000 and 0.05 to get 25000.

$$\frac{1}{37500}-\frac{1}{25000}$$

Subtract \frac{1}{25000} from \frac{1}{37500} to get -\frac{1}{75000}.

$$-\frac{1}{75000}$$

Factor

$$-\frac{1}{75000} = -1.3333333333333333 \times 10^{-5}$$