Solve 0.1+1.96sqrt{0.1*0.9/100}

$$0.1+1.96 \sqrt{ \frac{ 0.1 \cdot 0.9 }{ 100 } }$$

Evaluate

$$0.1588$$

Solution Steps

Multiply 0.1 and 0.9 to get 0.09.

$$0.1+1.96\sqrt{\frac{0.09}{100}}$$

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

$$0.1+1.96\sqrt{\frac{9}{10000}}$$

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.

$$0.1+1.96\times \frac{3}{100}$$

Convert decimal number 1.96 to fraction \frac{196}{100}. Reduce the fraction \frac{196}{100} to lowest terms by extracting and canceling out 4.

$$0.1+\frac{49}{25}\times \frac{3}{100}$$

Multiply \frac{49}{25} times \frac{3}{100} by multiplying numerator times numerator and denominator times denominator.

$$0.1+\frac{49\times 3}{25\times 100}$$

Do the multiplications in the fraction \frac{49\times 3}{25\times 100}.

$$0.1+\frac{147}{2500}$$

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

$$\frac{1}{10}+\frac{147}{2500}$$

Least common multiple of 10 and 2500 is 2500. Convert \frac{1}{10} and \frac{147}{2500} to fractions with denominator 2500.

$$\frac{250}{2500}+\frac{147}{2500}$$

Since \frac{250}{2500} and \frac{147}{2500} have the same denominator, add them by adding their numerators.

$$\frac{250+147}{2500}$$

Add 250 and 147 to get 397.

$$\frac{397}{2500}$$

Factor

$$\frac{397}{2 ^ {2} \cdot 5 ^ {4}} = 0.1588$$