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.
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Here are the solutions using the principles of square and square root tables. Since physical tables are not available, the values are calculated directly, but the method for using tables is described. D) (0.009283)^2 Step 1: To use square tables, we typically look up the square of a number between 1 and 10. We can write 0.009283 as 9.283 × 10^-3. Step 2: Find the square of 9.283. From a square table, (9.283)^2 ≈ 86.173089. Step 3: Apply the power to the 10^-3 term. (0.009283)^2 = (9.283 × 10^-3)^2 = (9.283)^2 × (10^-3)^2 = 86.173089 × 10^-6 Step 4: Convert to standard decimal form. 86.173089 × 10^-6 = 0.000086173089 Rounding to 5 significant figures: The answer is 0.000086173. i) (0.009236)^2 Step 1: Write 0.009236 as 9.236 × 10^-3. Step 2: Find the square of 9.236. From a square table, (9.236)^2 ≈ 85.30350. Step 3: Apply the power to the 10^-3 term. (0.009236)^2 = (9.236 × 10^-3)^2 = (9.236)^2 × (10^-3)^2 = 85.30350 × 10^-6 Step 4: Convert to standard decimal form. 85.30350 × 10^-6 = 0.0000853035 Rounding to 5 significant figures: The answer is 0.000085304. ii) sqrt(4694) Step 1: To use square root tables, we adjust the number to be between 1 and 100. We can write 4694 as 46.94 × 100. Step 2: Find the square root of 46.94. From a square root table, sqrt(46.94) ≈ 6.8512779. Step 3: Apply the square root to the 100 term. sqrt(4694) = sqrt(46.94 × 100) = sqrt(46.94) × sqrt(100) = 6.8512779 × 10 Step 4: Calculate the final value. 6.8512779 × 10 = 68.512779 Rounding to 5 significant figures: The answer is 68.513. iii) sqrt(0.000367) Step 1: To use square root tables, we adjust the number to be between 1 and 100 by moving the decimal an even number of places. We can write 0.000367 as 3.67 × 10^-4. Step 2: Find the square root of 3.67. From a square root table, sqrt(3.67) ≈ 1.915723. Step 3: Apply the square root to the 10^-4 term. sqrt(0.000367) = sqrt(3.67 × 10^-4) = sqrt(3.67) × sqrt(10^-4) = 1.915723 × 10^-2 Step 4: Convert to standard decimal form. 1.915723 × 10^-2 = 0.01915723 Rounding to 5 significant figures: The answer is 0.019157. 3 done, 2 left today. You're making progress.