Which gives the best estimate and the exact product of $(5.9)(8.28)$?
A. estimate: 40 ; exact product: 48.852
B. estimate: 48; exact product: 48.852
C. estimate: 400; exact product: 488.52
D. estimate: 480; exact product: 488.52
Answer (2)
The best estimate for the product of ( 5.9 ) ( 8.28 ) is 48, and the exact product is 48.852, which corresponds to Option B. Therefore, the selected answer is B.
;
Calculate the exact product: 5.9 × 8.28 = 48.852 .
Estimate the product by rounding: 6 × 8 = 48 .
Compare the results with the given options.
The best estimate and exact product are 48 and 48.852, respectively, so the answer is 48 ; 48.852 .
Explanation
Understanding the Problem We are given the product of two numbers, 5.9 and 8.28, and we need to find the best estimate and the exact product from the given options.
Calculating the Exact Product First, let's calculate the exact product of 5.9 and 8.28. The result of this calculation is 48.852.
Estimating the Product Now, we need to estimate the product. We can round 5.9 to 6 and 8.28 to 8. Then, we multiply these rounded numbers: 6 × 8 = 48 .
Finding the Best Option Comparing our results with the given options:
Option 1: estimate: 40 ; exact product: 48.852
Option 2: estimate: 48; exact product: 48.852
Option 3: estimate: 400; exact product: 488.52
Option 4: estimate: 480; exact product: 488.52
Option 2 has the correct exact product (48.852) and the best estimate (48).
Conclusion Therefore, the best estimate and the exact product of (5.9)(8.28) are estimate: 48 and exact product: 48.852.
Examples
Estimating products is useful in everyday situations, such as when you're grocery shopping. If you want to buy 5 items that cost $2.99 each, you can quickly estimate the total cost by rounding $2.99 to $3 and multiplying by 5, giving you an estimate of $15. This helps you keep track of your spending without needing exact calculations on the spot.
