Solve 110.27-1.9628.95/sqrt{100}

$$110.27-1.96 \frac{ 28.95 }{ \sqrt{ 100 } }$$

Evaluate

$$104.5958$$

Solution Steps

Calculate the square root of 100 and get 10.

$$110.27-1.96\times \frac{28.95}{10}$$

Expand \frac{28.95}{10} by multiplying both numerator and the denominator by 100.

$$110.27-1.96\times \frac{2895}{1000}$$

Reduce the fraction \frac{2895}{1000} to lowest terms by extracting and canceling out 5.

$$110.27-1.96\times \frac{579}{200}$$

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.

$$110.27-\frac{49}{25}\times \frac{579}{200}$$

Multiply \frac{49}{25} times \frac{579}{200} by multiplying numerator times numerator and denominator times denominator.

$$110.27-\frac{49\times 579}{25\times 200}$$

Do the multiplications in the fraction \frac{49\times 579}{25\times 200}.

$$110.27-\frac{28371}{5000}$$

Convert decimal number 110.27 to fraction \frac{11027}{100}.

$$\frac{11027}{100}-\frac{28371}{5000}$$

Least common multiple of 100 and 5000 is 5000. Convert \frac{11027}{100} and \frac{28371}{5000} to fractions with denominator 5000.

$$\frac{551350}{5000}-\frac{28371}{5000}$$

Since \frac{551350}{5000} and \frac{28371}{5000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{551350-28371}{5000}$$

Subtract 28371 from 551350 to get 522979.

$$\frac{522979}{5000}$$

Factor

$$\frac{173 \cdot 3023}{2 ^ {3} \cdot 5 ^ {4}} = 104\frac{2979}{5000} = 104.5958$$