Solve .9-.8/sqrt{frac{.8left(1-.8right){100}}}

$$\frac{ .9-.8 }{ \sqrt{ \frac{ .8 \left( 1-.8 \right) }{ 100 } } }$$

Evaluate

$$2.5$$

Solution Steps

Subtract 0.8 from 0.9 to get 0.1.

$$\frac{0.1}{\sqrt{\frac{0.8\left(1-0.8\right)}{100}}}$$

Subtract 0.8 from 1 to get 0.2.

$$\frac{0.1}{\sqrt{\frac{0.8\times 0.2}{100}}}$$

Multiply 0.8 and 0.2 to get 0.16.

$$\frac{0.1}{\sqrt{\frac{0.16}{100}}}$$

Expand \frac{0.16}{100} by multiplying both numerator and the denominator by 100.

$$\frac{0.1}{\sqrt{\frac{16}{10000}}}$$

Reduce the fraction \frac{16}{10000} to lowest terms by extracting and canceling out 16.

$$\frac{0.1}{\sqrt{\frac{1}{625}}}$$

Rewrite the square root of the division \frac{1}{625} as the division of square roots \frac{\sqrt{1}}{\sqrt{625}}. Take the square root of both numerator and denominator.

$$\frac{0.1}{\frac{1}{25}}$$

Divide 0.1 by \frac{1}{25} by multiplying 0.1 by the reciprocal of \frac{1}{25}.

$$0.1\times 25$$

Multiply 0.1 and 25 to get 2.5.

$$2.5$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$