Solve 100(1-0.8%)/1-0.08

$$\frac { 100 ( 1 - 0.8 \% ) } { 1 - 0.08 }$$

Evaluate

$$\frac{2480}{23}\approx 107.826086957$$

Solution Steps

Expand \frac{0.8}{100} by multiplying both numerator and the denominator by 10.

$$\frac{100\left(1-\frac{8}{1000}\right)}{1-0.08}$$

Reduce the fraction \frac{8}{1000} to lowest terms by extracting and canceling out 8.

$$\frac{100\left(1-\frac{1}{125}\right)}{1-0.08}$$

Convert 1 to fraction \frac{125}{125}.

$$\frac{100\left(\frac{125}{125}-\frac{1}{125}\right)}{1-0.08}$$

Since \frac{125}{125} and \frac{1}{125} have the same denominator, subtract them by subtracting their numerators.

$$\frac{100\times \frac{125-1}{125}}{1-0.08}$$

Subtract 1 from 125 to get 124.

$$\frac{100\times \frac{124}{125}}{1-0.08}$$

Express 100\times \frac{124}{125} as a single fraction.

$$\frac{\frac{100\times 124}{125}}{1-0.08}$$

Multiply 100 and 124 to get 12400.

$$\frac{\frac{12400}{125}}{1-0.08}$$

Reduce the fraction \frac{12400}{125} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{496}{5}}{1-0.08}$$

Subtract 0.08 from 1 to get 0.92.

$$\frac{\frac{496}{5}}{0.92}$$

Express \frac{\frac{496}{5}}{0.92} as a single fraction.

$$\frac{496}{5\times 0.92}$$

Multiply 5 and 0.92 to get 4.6.

$$\frac{496}{4.6}$$

Expand \frac{496}{4.6} by multiplying both numerator and the denominator by 10.

$$\frac{4960}{46}$$

Reduce the fraction \frac{4960}{46} to lowest terms by extracting and canceling out 2.

$$\frac{2480}{23}$$

Factor

$$\frac{5 \cdot 31 \cdot 2 ^ {4}}{23} = 107\frac{19}{23} = 107.82608695652173$$