Solve 4-10^-20/2-10^-10

$$\frac { 4 - 10 ^ { - 20 } } { 2 - 10 ^ { - 10 } }$$

Evaluate

$$\frac{20000000001}{10000000000}=2$$

Solution Steps

Calculate 10 to the power of -20 and get \frac{1}{100000000000000000000}.

$$\frac{4-\frac{1}{100000000000000000000}}{2-10^{-10}}$$

Subtract \frac{1}{100000000000000000000} from 4 to get \frac{399999999999999999999}{100000000000000000000}.

$$\frac{\frac{399999999999999999999}{100000000000000000000}}{2-10^{-10}}$$

Calculate 10 to the power of -10 and get \frac{1}{10000000000}.

$$\frac{\frac{399999999999999999999}{100000000000000000000}}{2-\frac{1}{10000000000}}$$

Subtract \frac{1}{10000000000} from 2 to get \frac{19999999999}{10000000000}.

$$\frac{\frac{399999999999999999999}{100000000000000000000}}{\frac{19999999999}{10000000000}}$$

Divide \frac{399999999999999999999}{100000000000000000000} by \frac{19999999999}{10000000000} by multiplying \frac{399999999999999999999}{100000000000000000000} by the reciprocal of \frac{19999999999}{10000000000}.

$$\frac{399999999999999999999}{100000000000000000000}\times \frac{10000000000}{19999999999}$$

Multiply \frac{399999999999999999999}{100000000000000000000} and \frac{10000000000}{19999999999} to get \frac{20000000001}{10000000000}.

$$\frac{20000000001}{10000000000}$$

Factor

$$\frac{3 \cdot 19 \cdot 1627 \cdot 215659}{2 ^ {10} \cdot 5 ^ {10}} = 2\frac{1}{10000000000} = 2.0000000001$$