Select the correct answer.
What is the solution to the problem expressed to the correct number of significant figures?
[tex]$15.11+(142 \times 16.5)=?$
A. 2,358
B. [tex]$2,358.1$
C. 2,360
D. 2,400
Answer (1)
Multiply 142 × 16.5 = 2343 .
Round the result to 3 significant figures: 2343 ≈ 2340 .
Add 15.11 + 2340 = 2355.11 .
Round the result to the tens place: 2355.11 ≈ 2360 . The final answer is 2 , 360 .
Explanation
Problem Analysis We are asked to calculate 15.11 + ( 142 × 16.5 ) and express the result to the correct number of significant figures.
Multiplication First, we perform the multiplication 142 × 16.5 = 2343 . Since 142 and 16.5 both have 3 significant figures, the result of the multiplication should be rounded to 3 significant figures. Thus, 2343 becomes 2340 .
Addition Next, we perform the addition 15.11 + 2340 = 2355.11 . Since 2340 is rounded to the tens place, we round the result to the tens place as well. Thus, 2355.11 becomes 2360 .
Final Answer Therefore, the solution to the problem expressed to the correct number of significant figures is 2,360.
Examples
When calculating the total cost of items in a store, each with a slightly different price and quantity, it's important to consider significant figures to avoid overstating the precision of the total. For example, if you buy 142 items that cost $16.5 each, and then add a $15.11 tax, using significant figures ensures that the final cost reflects the accuracy of the initial measurements and calculations. This prevents misleading financial reports and ensures realistic budgeting.
