This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Calculate the true length of each piece of wood. The total length of the wood is 2 m, and it is cut into 3 equal parts. True length of each piece = (2)/(3) m. Step 2: Identify the approximated length. The carpenter approximates the length of each piece to 0.66 m. Step 3: Calculate the absolute error. Absolute error is the absolute difference between the true value and the approximated value. Absolute error = | (2)/(3) - 0.66 | To perform the subtraction, convert 0.66 to a fraction: 0.66 = (66)/(100) = (33)/(50). Absolute error = | (2)/(3) - (33)/(50) | Find a common denominator, which is 150: Absolute error = | (2 × 50)/(3 × 50) - (33 × 3)/(50 × 3) | Absolute error = | (100)/(150) - (99)/(150) | Absolute error = | (1)/(150) | = (1)/(150) m. Step 4: Calculate the percentage error. The formula for percentage error is: Percentage Error = Absolute ErrorTrue Value × 100\% Percentage Error = (1)/(150)(2)/(3) × 100\% Percentage Error = (1)/(150) × (3)/(2) × 100\% Percentage Error = (3)/(300) × 100\% Percentage Error = (1)/(100) × 100\% Percentage Error = 1\% The percentage error due to this approximation is 1\%. That's 2 down. 3 left today — send the next one.