Question

Evaluate the following expression: \[ \frac{0.963 \times 0.963 - 0.963 \times 0.037 + 0.037 \times 0.037}{0.963 \times 0.963 \times 0.963 + 0.037 \times 0.037 \times 0.037} \]

• A. \( -1 \)
• B. \( 0 \)
• C. \( 1 \)
• D. \( 2 \)

Hint:

Remember to break down complex expressions into manageable parts. Evaluate each operation step-by-step.

Answer 1

The Correct Option is C

Step 1: Simplifying the numerator: \[ 0.963 \times 0.963 = 0.927369, \quad 0.963 \times 0.037 = 0.035691, \quad 0.037 \times 0.037 = 0.001369 \] Thus, the numerator is: \[ 0.927369 - 0.035691 + 0.001369 = 0.893047 \] Step 2: Simplifying the denominator: \[ 0.963 \times 0.963 \times 0.963 = 0.894786, \quad 0.037 \times 0.037 \times 0.037 = 0.000050653 \] Thus, the denominator is: \[ 0.894786 + 0.000050653 = 0.894836653 \] Step 3: Dividing the numerator by the denominator: \[ \frac{0.893047}{0.894836653} \approx 1.000 \] Thus, the value of the expression is \( 1 \).