Express [tex]\sqrt{\frac{19}{20}}[/tex] as a decimal.
Answer (1)
Simplify the expression 20 19 .
Calculate the square root: 20 19 ≈ 0.97467943448 .
Round the result to five decimal places: 0.97468 .
The decimal representation of 20 19 is approximately 0.97468 .
Explanation
Understanding the problem We are asked to express 20 19 as a decimal. This means we need to find the decimal representation of the square root of the fraction 19/20.
Simplifying the expression First, let's simplify the fraction inside the square root. We have 20 19 . To get a decimal approximation, we can directly calculate the square root of the fraction.
Calculating the square root Using a calculator, we find that 20 19 ≈ 0.97467943448 .
Rounding the result We can round this to a reasonable number of decimal places, such as five decimal places, to get 0.97468 .
Examples
Understanding how to convert fractions and square roots to decimals is useful in many real-world situations. For example, if you are calculating the efficiency of a machine, you might end up with a fraction inside a square root. Converting this to a decimal allows you to easily understand and compare the efficiency value. Also, in construction or engineering, you might need to calculate the length of a diagonal using the Pythagorean theorem, which involves square roots. Expressing these lengths as decimals makes them easier to measure and work with.
