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

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

Evaluate

$$-\frac{\sqrt{10000}}{30}\approx -3.333333333$$

Solution Steps

Subtract 0.9 from 0.8 to get -0.1.

$$\frac{-0.1}{\sqrt{\frac{0.9\left(1-0.9\right)}{100}}}$$

Subtract 0.9 from 1 to get 0.1.

$$\frac{-0.1}{\sqrt{\frac{0.9\times 0.1}{100}}}$$

Multiply 0.9 and 0.1 to get 0.09.

$$\frac{-0.1}{\sqrt{\frac{0.09}{100}}}$$

Expand \frac{0.09}{100} by multiplying both numerator and the denominator by 100.

$$\frac{-0.1}{\sqrt{\frac{9}{10000}}}$$

Rewrite the square root of the division \frac{9}{10000} as the division of square roots \frac{\sqrt{9}}{\sqrt{10000}}. Take the square root of both numerator and denominator.

$$\frac{-0.1}{\frac{3}{100}}$$

Divide -0.1 by \frac{3}{100} by multiplying -0.1 by the reciprocal of \frac{3}{100}.

$$-0.1\times \frac{100}{3}$$

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

$$-\frac{1}{10}\times \frac{100}{3}$$

Multiply -\frac{1}{10} times \frac{100}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-100}{10\times 3}$$

Do the multiplications in the fraction \frac{-100}{10\times 3}.

$$\frac{-100}{30}$$

Reduce the fraction \frac{-100}{30} to lowest terms by extracting and canceling out 10.

$$-\frac{10}{3}$$