Solve 10.998-2.5750.02/sqrt{100}

$$10.998-2.575 \frac{ 0.02 }{ \sqrt{ 100 } }$$

Evaluate

$$10.99285$$

Solution Steps

Calculate the square root of 100 and get 10.

$$10.998-2.575\times \frac{0.02}{10}$$

Expand \frac{0.02}{10} by multiplying both numerator and the denominator by 100.

$$10.998-2.575\times \frac{2}{1000}$$

Reduce the fraction \frac{2}{1000} to lowest terms by extracting and canceling out 2.

$$10.998-2.575\times \frac{1}{500}$$

Convert decimal number 2.575 to fraction \frac{2575}{1000}. Reduce the fraction \frac{2575}{1000} to lowest terms by extracting and canceling out 25.

$$10.998-\frac{103}{40}\times \frac{1}{500}$$

Multiply \frac{103}{40} times \frac{1}{500} by multiplying numerator times numerator and denominator times denominator.

$$10.998-\frac{103\times 1}{40\times 500}$$

Do the multiplications in the fraction \frac{103\times 1}{40\times 500}.

$$10.998-\frac{103}{20000}$$

Convert decimal number 10.998 to fraction \frac{10998}{1000}. Reduce the fraction \frac{10998}{1000} to lowest terms by extracting and canceling out 2.

$$\frac{5499}{500}-\frac{103}{20000}$$

Least common multiple of 500 and 20000 is 20000. Convert \frac{5499}{500} and \frac{103}{20000} to fractions with denominator 20000.

$$\frac{219960}{20000}-\frac{103}{20000}$$

Since \frac{219960}{20000} and \frac{103}{20000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{219960-103}{20000}$$

Subtract 103 from 219960 to get 219857.

$$\frac{219857}{20000}$$

Factor

$$\frac{23 \cdot 79 \cdot 11 ^ {2}}{2 ^ {5} \cdot 5 ^ {4}} = 10\frac{19857}{20000} = 10.99285$$