Solve frac{2*10^{7}*(1,2*10^{-3}-8*10^-4)}{(2,4*10^2+8,76*10^3):2,25*10^5}

$$\frac { 2 \times 10 ^ { 7 } \times ( 1,2 \times 10 ^ { - 3 } - 8 \times 10 ^ { - 4 } ) } { ( 2,4 \times 10 ^ { 2 } + 8,76 \times 10 ^ { 3 } ) : 2,25 \times 10 ^ { 5 } }$$

Evaluate

$$0,00002$$

Solution Steps

Calculate 10 to the power of 7 and get 10000000.

$$\frac{2\times 10000000\left(1,2\times 10^{-3}-8\times 10^{-4}\right)}{\frac{2,4\times 10^{2}+8,76\times 10^{3}}{2,25}\times 10^{5}}$$

Multiply 2 and 10000000 to get 20000000.

$$\frac{20000000\left(1,2\times 10^{-3}-8\times 10^{-4}\right)}{\frac{2,4\times 10^{2}+8,76\times 10^{3}}{2,25}\times 10^{5}}$$

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

$$\frac{20000000\left(1,2\times \frac{1}{1000}-8\times 10^{-4}\right)}{\frac{2,4\times 10^{2}+8,76\times 10^{3}}{2,25}\times 10^{5}}$$

Multiply 1,2 and \frac{1}{1000} to get \frac{3}{2500}.

$$\frac{20000000\left(\frac{3}{2500}-8\times 10^{-4}\right)}{\frac{2,4\times 10^{2}+8,76\times 10^{3}}{2,25}\times 10^{5}}$$

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

$$\frac{20000000\left(\frac{3}{2500}-8\times \frac{1}{10000}\right)}{\frac{2,4\times 10^{2}+8,76\times 10^{3}}{2,25}\times 10^{5}}$$

Multiply 8 and \frac{1}{10000} to get \frac{1}{1250}.

$$\frac{20000000\left(\frac{3}{2500}-\frac{1}{1250}\right)}{\frac{2,4\times 10^{2}+8,76\times 10^{3}}{2,25}\times 10^{5}}$$

Subtract \frac{1}{1250} from \frac{3}{2500} to get \frac{1}{2500}.

$$\frac{20000000\times \frac{1}{2500}}{\frac{2,4\times 10^{2}+8,76\times 10^{3}}{2,25}\times 10^{5}}$$

Multiply 20000000 and \frac{1}{2500} to get 8000.

$$\frac{8000}{\frac{2,4\times 10^{2}+8,76\times 10^{3}}{2,25}\times 10^{5}}$$

Calculate 10 to the power of 2 and get 100.

$$\frac{8000}{\frac{2,4\times 100+8,76\times 10^{3}}{2,25}\times 10^{5}}$$

Multiply 2,4 and 100 to get 240.

$$\frac{8000}{\frac{240+8,76\times 10^{3}}{2,25}\times 10^{5}}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{8000}{\frac{240+8,76\times 1000}{2,25}\times 10^{5}}$$

Multiply 8,76 and 1000 to get 8760.

$$\frac{8000}{\frac{240+8760}{2,25}\times 10^{5}}$$

Add 240 and 8760 to get 9000.

$$\frac{8000}{\frac{9000}{2,25}\times 10^{5}}$$

Expand \frac{9000}{2,25} by multiplying both numerator and the denominator by 100.

$$\frac{8000}{\frac{900000}{225}\times 10^{5}}$$

Divide 900000 by 225 to get 4000.

$$\frac{8000}{4000\times 10^{5}}$$

Calculate 10 to the power of 5 and get 100000.

$$\frac{8000}{4000\times 100000}$$

Multiply 4000 and 100000 to get 400000000.

$$\frac{8000}{400000000}$$

Reduce the fraction \frac{8000}{400000000} to lowest terms by extracting and canceling out 8000.

$$\frac{1}{50000}$$

Factor

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