Solve 1/0.1+frac{1-01{10000}}

$$\frac { 1 } { 0.1 + \frac { 1 - 01 } { 10000 } }$$

Evaluate

$$\frac{10000}{1001}\approx 9.99000999$$

Solution Steps

Multiply 0 and 1 to get 0.

$$\frac{1}{0.1+\frac{1-0}{10000}}$$

Subtract 0 from 1 to get 1.

$$\frac{1}{0.1+\frac{1}{10000}}$$

Convert decimal number 0.1 to fraction \frac{1}{10}.

$$\frac{1}{\frac{1}{10}+\frac{1}{10000}}$$

Least common multiple of 10 and 10000 is 10000. Convert \frac{1}{10} and \frac{1}{10000} to fractions with denominator 10000.

$$\frac{1}{\frac{1000}{10000}+\frac{1}{10000}}$$

Since \frac{1000}{10000} and \frac{1}{10000} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{1000+1}{10000}}$$

Add 1000 and 1 to get 1001.

$$\frac{1}{\frac{1001}{10000}}$$

Divide 1 by \frac{1001}{10000} by multiplying 1 by the reciprocal of \frac{1001}{10000}.

$$1\times \frac{10000}{1001}$$

Multiply 1 and \frac{10000}{1001} to get \frac{10000}{1001}.

$$\frac{10000}{1001}$$

Factor

$$\frac{2 ^ {4} \cdot 5 ^ {4}}{7 \cdot 11 \cdot 13} = 9\frac{991}{1001} = 9.99000999000999$$