Select the correct answer.
What is the solution to the problem expressed to the correct number of significant figures? [tex]$1511+(142 \times 16.5)=?$
Answer (1)
Calculate the product: 142 × 16.5 = 2343 .
Round the product to 3 significant figures: 2340.
Add the rounded product to 1511: 1511 + 2340 = 3851 .
Round the sum to the tens place: 3850. However, none of the options match this result, indicating a possible error in the question or options.
Re-evaluating the options, the closest answer based on significant figures is not available. There is an error in the question or the options.
Explanation
Calculate the product We need to calculate 1511 + ( 142 × 16.5 ) and express the answer to the correct number of significant figures. First, we perform the multiplication: 142 × 16.5 = 2343 .
Consider significant figures for multiplication Now we consider significant figures. 142 has 3 significant figures, and 16.5 has 3 significant figures. Therefore, their product should be rounded to 3 significant figures. So, 2343 is rounded to 2340.
Perform the addition Next, we perform the addition: 1511 + 2340 = 3851 .
Consider significant figures for addition Now we consider significant figures for addition. 1511 has no digits after the decimal point (it's an integer), and 2340 also has no digits after the decimal point. Therefore, the result of the addition should be rounded to the ones place. The result 3851 is rounded to the nearest hundred, which is 3900.
Final Answer Therefore, the solution to the problem expressed to the correct number of significant figures is 3900. However, this is not one of the options. Let's re-evaluate the rounding. When we rounded 2343 to 3 significant figures, we got 2340. Then we added 1511 to 2340, getting 3851. Since both numbers we added (1511 and 2340) are only accurate to the ones place, our answer should also be accurate to the ones place. Thus, we round 3851 to the nearest hundred, which is 3900. However, the options provided do not include 3900. Let's look at the initial multiplication result without rounding to significant figures: 2343. Adding this to 1511 gives 3854. Now, we need to consider the significant figures. 142 and 16.5 both have 3 significant figures. Therefore, the product 2343 should be rounded to 3 significant figures, which is 2340. Then, we add 1511. Since 1511 has 4 significant figures and 2340 has 3 significant figures, we should consider the place values. 1511 is accurate to the ones place, and 2340 is accurate to the tens place. Therefore, the result should be rounded to the tens place. So, 3851 should be rounded to the nearest ten, which is 3850. However, this is still not an option. Let's analyze the options given. Option A is 2358, Option B is 2350, Option C is 2360, and Option D is 2400. The closest option to our initial calculation of 3854 is not among the choices. There seems to be an error in the problem statement or the options provided. However, if we consider only the multiplication, 142 × 16.5 = 2343 . Rounding this to 2 significant figures gives 2300, which is not an option. Rounding to 3 significant figures gives 2340. If the question was 142 × 16.5 = ? , then the answer would be 2340. However, the question is 1511 + ( 142 × 16.5 ) = ? . The multiplication gives 2343, which rounds to 2340. Adding 1511 gives 3851. Rounding to the nearest hundred gives 3900. None of the options are correct.
Re-evaluating the options Given the options, let's reconsider the significant figures. 142 × 16.5 = 2343 . Since both numbers have 3 significant figures, the result should have 3 significant figures, so 2340. Then 1511 + 2340 = 3851 . Since 1511 is accurate to the ones place and 2340 is accurate to the tens place, the result should be rounded to the tens place, which is 3850. However, this is not an option. If we round to the hundreds place, we get 3900. The closest option is C. 2,360, if we are only considering the multiplication part. However, this is incorrect. If we round 3851 to two significant figures, we get 3900. If we round to one significant figure, we get 4000. The closest option is D. 2,400, which is incorrect. There is an error in the question or the options.
Examples
Understanding significant figures is crucial in scientific measurements. For example, if you are measuring the length of a table and one measurement is 1.5 meters and another is 1.55 meters, knowing how to combine these measurements accurately ensures your calculations, like area or volume, reflect the true precision of your data. This prevents overstating the accuracy of your results, which is vital in engineering, physics, and chemistry.
