Express $\sqrt{\frac{19}{20}}$ as a decimal.
Answer (2)
Calculate the value of the fraction inside the square root: 20 19 .
Take the square root of the result: 20 19 ≈ 0.974679 .
Round the result to a reasonable number of decimal places.
The decimal representation of 20 19 is approximately 0.9747 .
Explanation
Understanding the Problem We are asked to express 20 19 as a decimal. This involves finding the square root of a fraction and converting it to its decimal representation.
Calculating the Decimal Value To simplify the calculation, we can directly compute the decimal value of the expression 20 19 .
Finding the Decimal Approximation Using a calculator (or the python tool), we find that 20 19 ≈ 0.9746794344808963 . Rounding this to a reasonable number of decimal places, such as four, gives us 0.9747.
Final Answer Therefore, 20 19 expressed as a decimal is approximately 0.9747.
Examples
Understanding how to convert fractions within square roots to decimals is useful in various real-world scenarios. For example, when calculating electrical impedance in AC circuits, you often encounter complex numbers involving square roots of fractions. Similarly, in physics, you might need to calculate the refractive index of a material, which can involve square roots of fractional values. Knowing how to quickly convert these to decimals allows for easier comparison and analysis of the results.
The decimal representation of 20 19 is approximately 0.9747 . This is calculated by taking the square root of the fraction, which gives us a value that can be rounded to four decimal places. Thus, 20 19 ≈ 0.9747 .
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