When performing the calculation \( (102-27.48)^{*} 4.71 \), what is the correct answer, to the proper number of significant figures? 350.989 350 351.0 350.99 351

We want to evaluate   (102 – 27.48) × 4.71 and then round the final answer to the proper number of significant figures. Step 1. Subtraction (102 – 27.48): For subtraction the rule is not “number of sig. figs” but “decimal places.” Look at the given numbers:  • 102 is written with no decimal (i.e. to the nearest unit)  • 27.48 is to two decimal places. When subtracting, the answer should be rounded to the least precise decimal place—the ones place. Although the exact difference is   102 – 27.48 = 74.52 we must keep in mind that 102 is only known to the nearest whole number. (It is better to carry extra digits in intermediate steps and round only at the end.) In this case we note the uncertainty, but we will do the multiplication with extra digits and then finally round. Step 2. Multiplication: Now multiply the difference by 4.71:   74.52 × 4.71 ≈ 350.9892 When multiplying, the result should have as many significant figures as the factor with the fewest significant figures. Look at the original numbers:  • 102 has 3 significant figures.  • 27.48 has 4 significant figures.  • 4.71 has 3 significant figures. Even though the subtraction “lost” decimal places, in a combined operation you are advised to retain extra digits in intermediate steps and then round off at the end according to the multiplication rule. The multiplication step tells us to use 3 significant figures (because the least among them is 3). Step 3. Rounding the final result to 3 significant figures: 350.9892 rounded to 3 significant figures:   The first three digits are “3”, “5”, and “0” (i.e. 350). To decide whether 350 rounds up or stays the same, we look at the next digit (9, which is 5 or greater). Thus 350.989 rounds to 351 (since 350.989 is closer to 351 than 350). Thus, the correctly rounded answer is 351. Answer: 351