Solve 10^8-10/10^6-10^10-1/10^9

$$\frac { 10 ^ { 8 } - 10 } { 10 ^ { 6 } } - \frac { 10 ^ { 10 } - 1 } { 10 ^ { 9 } }$$

Evaluate

$$\frac{89999990001}{1000000000}=89.999990001$$

Solution Steps

Calculate 10 to the power of 8 and get 100000000.

$$\frac{100000000-10}{10^{6}}-\frac{10^{10}-1}{10^{9}}$$

Subtract 10 from 100000000 to get 99999990.

$$\frac{99999990}{10^{6}}-\frac{10^{10}-1}{10^{9}}$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{99999990}{1000000}-\frac{10^{10}-1}{10^{9}}$$

Reduce the fraction \frac{99999990}{1000000} to lowest terms by extracting and canceling out 10.

$$\frac{9999999}{100000}-\frac{10^{10}-1}{10^{9}}$$

Calculate 10 to the power of 10 and get 10000000000.

$$\frac{9999999}{100000}-\frac{10000000000-1}{10^{9}}$$

Subtract 1 from 10000000000 to get 9999999999.

$$\frac{9999999}{100000}-\frac{9999999999}{10^{9}}$$

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{9999999}{100000}-\frac{9999999999}{1000000000}$$

Least common multiple of 100000 and 1000000000 is 1000000000. Convert \frac{9999999}{100000} and \frac{9999999999}{1000000000} to fractions with denominator 1000000000.

$$\frac{99999990000}{1000000000}-\frac{9999999999}{1000000000}$$

Since \frac{99999990000}{1000000000} and \frac{9999999999}{1000000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{99999990000-9999999999}{1000000000}$$

Subtract 9999999999 from 99999990000 to get 89999990001.

$$\frac{89999990001}{1000000000}$$

Factor

$$\frac{3 ^ {3} \cdot 19 \cdot 175438577}{2 ^ {9} \cdot 5 ^ {9}} = 89\frac{999990001}{1000000000} = 89.999990001$$