Solve 1/10*1/100-{left(-frac{1/10right)}^2}{sqrt{1/100}}

$$\frac{ \frac{ 1 }{ 10 } \times \frac{ 1 }{ 100 } - { \left(- \frac{ 1 }{ 10 } \right) }^{ 2 } }{ \sqrt{ \frac{ 1 }{ 100 } } }$$

Evaluate

$$-\frac{9\sqrt{100}}{1000}\approx -0.09$$

Solution Steps

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

$$\frac{\frac{1\times 1}{10\times 100}-\left(-\frac{1}{10}\right)^{2}}{\sqrt{\frac{1}{100}}}$$

Do the multiplications in the fraction \frac{1\times 1}{10\times 100}.

$$\frac{\frac{1}{1000}-\left(-\frac{1}{10}\right)^{2}}{\sqrt{\frac{1}{100}}}$$

Calculate -\frac{1}{10} to the power of 2 and get \frac{1}{100}.

$$\frac{\frac{1}{1000}-\frac{1}{100}}{\sqrt{\frac{1}{100}}}$$

Least common multiple of 1000 and 100 is 1000. Convert \frac{1}{1000} and \frac{1}{100} to fractions with denominator 1000.

$$\frac{\frac{1}{1000}-\frac{10}{1000}}{\sqrt{\frac{1}{100}}}$$

Since \frac{1}{1000} and \frac{10}{1000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-10}{1000}}{\sqrt{\frac{1}{100}}}$$

Subtract 10 from 1 to get -9.

$$\frac{-\frac{9}{1000}}{\sqrt{\frac{1}{100}}}$$

Rewrite the square root of the division \frac{1}{100} as the division of square roots \frac{\sqrt{1}}{\sqrt{100}}. Take the square root of both numerator and denominator.

$$\frac{-\frac{9}{1000}}{\frac{1}{10}}$$

Divide -\frac{9}{1000} by \frac{1}{10} by multiplying -\frac{9}{1000} by the reciprocal of \frac{1}{10}.

$$-\frac{9}{1000}\times 10$$

Express -\frac{9}{1000}\times 10 as a single fraction.

$$\frac{-9\times 10}{1000}$$

Multiply -9 and 10 to get -90.

$$\frac{-90}{1000}$$

Reduce the fraction \frac{-90}{1000} to lowest terms by extracting and canceling out 10.

$$-\frac{9}{100}$$