Solve 1000*2-10^-610/42.3*3.14*2*10^-3

$$\frac{ 1000 \cdot 2- { 10 }^{ -6 } 10 }{ 42.3 \cdot 3.14 \cdot 2 \times { 10 }^{ -3 } }$$

Evaluate

$$\frac{999999995}{132822}\approx 7528.873191188$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -6 and 1 to get -5.

$$\frac{1000\times 2-10^{-5}}{42.3\times 3.14\times 2\times 10^{-3}}$$

Multiply 1000 and 2 to get 2000.

$$\frac{2000-10^{-5}}{42.3\times 3.14\times 2\times 10^{-3}}$$

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$\frac{2000-\frac{1}{100000}}{42.3\times 3.14\times 2\times 10^{-3}}$$

Subtract \frac{1}{100000} from 2000 to get \frac{199999999}{100000}.

$$\frac{\frac{199999999}{100000}}{42.3\times 3.14\times 2\times 10^{-3}}$$

Multiply 42.3 and 3.14 to get 132.822.

$$\frac{\frac{199999999}{100000}}{132.822\times 2\times 10^{-3}}$$

Multiply 132.822 and 2 to get 265.644.

$$\frac{\frac{199999999}{100000}}{265.644\times 10^{-3}}$$

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

$$\frac{\frac{199999999}{100000}}{265.644\times \frac{1}{1000}}$$

Multiply 265.644 and \frac{1}{1000} to get \frac{66411}{250000}.

$$\frac{\frac{199999999}{100000}}{\frac{66411}{250000}}$$

Divide \frac{199999999}{100000} by \frac{66411}{250000} by multiplying \frac{199999999}{100000} by the reciprocal of \frac{66411}{250000}.

$$\frac{199999999}{100000}\times \frac{250000}{66411}$$

Multiply \frac{199999999}{100000} and \frac{250000}{66411} to get \frac{999999995}{132822}.

$$\frac{999999995}{132822}$$

Factor

$$\frac{5 \cdot 89 \cdot 1447 \cdot 1553}{2 \cdot 47 \cdot 157 \cdot 3 ^ {2}} = 7528\frac{115979}{132822} = 7528.873191188207$$