Solve 0.5+1.96sqrt{0.5*0.5/2500}

$$0.5+1.96 \sqrt{ \frac{ 0.5 \cdot 0.5 }{ 2500 } }$$

Evaluate

$$0.5196$$

Solution Steps

Multiply 0.5 and 0.5 to get 0.25.

$$0.5+1.96\sqrt{\frac{0.25}{2500}}$$

Expand \frac{0.25}{2500} by multiplying both numerator and the denominator by 100.

$$0.5+1.96\sqrt{\frac{25}{250000}}$$

Reduce the fraction \frac{25}{250000} to lowest terms by extracting and canceling out 25.

$$0.5+1.96\sqrt{\frac{1}{10000}}$$

Rewrite the square root of the division \frac{1}{10000} as the division of square roots \frac{\sqrt{1}}{\sqrt{10000}}. Take the square root of both numerator and denominator.

$$0.5+1.96\times \frac{1}{100}$$

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.

$$0.5+\frac{49}{25}\times \frac{1}{100}$$

Multiply \frac{49}{25} times \frac{1}{100} by multiplying numerator times numerator and denominator times denominator.

$$0.5+\frac{49\times 1}{25\times 100}$$

Do the multiplications in the fraction \frac{49\times 1}{25\times 100}.

$$0.5+\frac{49}{2500}$$

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}+\frac{49}{2500}$$

Least common multiple of 2 and 2500 is 2500. Convert \frac{1}{2} and \frac{49}{2500} to fractions with denominator 2500.

$$\frac{1250}{2500}+\frac{49}{2500}$$

Since \frac{1250}{2500} and \frac{49}{2500} have the same denominator, add them by adding their numerators.

$$\frac{1250+49}{2500}$$

Add 1250 and 49 to get 1299.

$$\frac{1299}{2500}$$

Factor

$$\frac{3 \cdot 433}{2 ^ {2} \cdot 5 ^ {4}} = 0.5196$$