The Correct Answer and Explanation is:
The correct answer is 0.5080.
To evaluate the expression √(0.0961 / (4.0836 – 3.7112)) and provide the answer correct to four decimal places, we must follow the standard order of operations. The calculation can be broken down into a series of clear steps.
First, we resolve the operation inside the parentheses, which is the subtraction in the denominator of the fraction. This is the initial step to simplify the overall expression.
4.0836 – 3.7112 = 0.3724.
After performing this subtraction, the expression simplifies to √(0.0961 / 0.3724).
Next, we perform the division operation that is inside the square root symbol. We divide the numerator by the result we just calculated for the denominator.
0.0961 ÷ 0.3724 ≈ 0.25805585.
It is good practice to keep several decimal places during intermediate steps to maintain precision for the final rounding. This calculation gives us the single value under the square root.
The third step is to calculate the square root of the result from the division.
√0.25805585… ≈ 0.50799198…
This provides the unrounded value of the entire expression.
Finally, the question requires the answer to be corrected to four decimal places. To achieve this, we examine the fifth digit after the decimal point in our calculated value, which is 0.50799198… The fifth decimal place is 9. The rule for rounding states that if this digit is 5 or greater, we round up the fourth decimal digit. Here, the fourth digit is 9. When we round up 9, it becomes 10, so we place a 0 in the fourth decimal position and carry over 1 to the third decimal position. This changes the 7 to an 8. Consequently, the value 0.50799… rounded to four decimal places becomes 0.5080.
