Solve 0.5*1*(1+10*4*10^-5)/1+10*2*10^-5

$$\frac { 0.5 \times 1 \times ( 1 + 10 \times 4 \times 10 ^ { - 5 } ) } { 1 + 10 \times 2 \times 10 ^ { - 5 } }$$

Evaluate

$$\frac{2501}{5001}\approx 0.50009998$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and -5 to get -4.

$$\frac{0.5\times 1\left(1+10^{-4}\times 4\right)}{1+10\times 2\times 10^{-5}}$$

To multiply powers of the same base, add their exponents. Add 1 and -5 to get -4.

$$\frac{0.5\times 1\left(1+10^{-4}\times 4\right)}{1+10^{-4}\times 2}$$

Multiply 0.5 and 1 to get 0.5.

$$\frac{0.5\left(1+10^{-4}\times 4\right)}{1+10^{-4}\times 2}$$

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

$$\frac{0.5\left(1+\frac{1}{10000}\times 4\right)}{1+10^{-4}\times 2}$$

Multiply \frac{1}{10000} and 4 to get \frac{1}{2500}.

$$\frac{0.5\left(1+\frac{1}{2500}\right)}{1+10^{-4}\times 2}$$

Add 1 and \frac{1}{2500} to get \frac{2501}{2500}.

$$\frac{0.5\times \frac{2501}{2500}}{1+10^{-4}\times 2}$$

Multiply 0.5 and \frac{2501}{2500} to get \frac{2501}{5000}.

$$\frac{\frac{2501}{5000}}{1+10^{-4}\times 2}$$

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

$$\frac{\frac{2501}{5000}}{1+\frac{1}{10000}\times 2}$$

Multiply \frac{1}{10000} and 2 to get \frac{1}{5000}.

$$\frac{\frac{2501}{5000}}{1+\frac{1}{5000}}$$

Add 1 and \frac{1}{5000} to get \frac{5001}{5000}.

$$\frac{\frac{2501}{5000}}{\frac{5001}{5000}}$$

Divide \frac{2501}{5000} by \frac{5001}{5000} by multiplying \frac{2501}{5000} by the reciprocal of \frac{5001}{5000}.

$$\frac{2501}{5000}\times \frac{5000}{5001}$$

Multiply \frac{2501}{5000} and \frac{5000}{5001} to get \frac{2501}{5001}.

$$\frac{2501}{5001}$$

Factor

$$\frac{41 \cdot 61}{3 \cdot 1667} = 0.5000999800039992$$