Deanna estimated the product of 6.45 and 10.2 below.
[tex]$(6.45)(10.2) \approx 6 \times 10=60$[/tex]
How does the estimate compare to the exact product?
A. The estimate is high because both factors are rounded down.
B. The estimate is low because both factors are rounded down.
C. The estimate is high because both factors are rounded up.
D. The estimate is low because both factors are rounded up.
Answer (2)
The estimate of 60 is lower than the exact product of 65.79, as both factors (6.45 and 10.2) were rounded down to 6 and 10, respectively. Thus, the correct choice is B. The estimate is low because both factors are rounded down.
;
Calculate the exact product: 6.45 × 10.2 = 65.79 .
Compare the estimate (60) with the exact product (65.79), noting that the estimate is lower.
Observe that 6.45 was rounded down to 6 and 10.2 was rounded down to 10.
Conclude that the estimate is low because both factors were rounded down. The answer is: The estimate is low because both factors are rounded down. T h ees t ima t e i s l o w b ec a u se b o t h f a c t ors a rero u n d e dd o w n .
Explanation
Problem Analysis We are asked to compare an estimate of the product of 6.45 and 10.2 with the exact product. The estimate is obtained by rounding each factor to the nearest whole number. We need to determine if the estimate is higher or lower than the exact product and explain why.
Calculate the Exact Product First, let's calculate the exact product of 6.45 and 10.2. The exact product is 6.45 × 10.2 = 65.79 .
Compare Estimate with Exact Product The estimate given is 6 × 10 = 60 . Comparing the estimate with the exact product, we see that 60 < 65.79 . Therefore, the estimate is lower than the exact product.
Analyze Rounding Direction Now, let's analyze how the estimate was obtained. The number 6.45 was rounded down to 6, and the number 10.2 was rounded down to 10. Since both factors were rounded down, the estimate is lower than the exact product.
Conclusion Therefore, the estimate is low because both factors are rounded down.
Examples
Estimating products is useful in everyday situations, such as when you are shopping and want to quickly calculate the total cost of several items. For example, if you are buying 5 items that cost $4.95 each, you can estimate the total cost by rounding $4.95 to $5 and multiplying by 5, giving you an estimate of $25. This allows you to quickly determine if you have enough money or if the total cost is within your budget. The same logic applies when estimating quantities or distances. For instance, if you need to travel 10.2 miles and you know you can drive about 6.45 miles per gallon, estimating the total gas needed can help you plan your trip effectively.
