Using compatible numbers, which is the best estimate of $(28.5)(7.1)$?
A. 36
B. 40
C. 210
D. 300
Answer (2)
The best estimate of ( 28.5 ) ( 7.1 ) using compatible numbers is 210 , obtained by rounding 28.5 to 30 and 7.1 to 7 before multiplying. This makes the mental calculation easier.
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Round 28.5 to 30 and 7.1 to 7 to use compatible numbers.
Multiply the rounded numbers: 30 × 7 = 210 .
The best estimate of ( 28.5 ) ( 7.1 ) is 210 .
Explanation
Understanding the Problem We are asked to estimate the product of 28.5 and 7.1 using compatible numbers. Compatible numbers are numbers that are easy to compute mentally.
Rounding to Compatible Numbers To estimate the product, we can round each number to a compatible number. We can round 28.5 to 30 and 7.1 to 7 . These numbers are compatible because they are easy to multiply.
Multiplying Compatible Numbers Now, we multiply the compatible numbers: 30 × 7 = 210 .
Comparing to Options The options are 36, 40, 210, and 300. Comparing our estimate of 210 to the options, we see that 210 is one of the options.
Final Answer Therefore, the best estimate of ( 28.5 ) ( 7.1 ) using compatible numbers is 210 .
Examples
Estimating with compatible numbers is useful in everyday situations, such as when you are shopping and want to quickly estimate the total cost of your items. For example, if you are buying 3 items that cost $9.75, $4.20, and $2.85, you can round these to $10, $4, and $3 respectively. Then, you can quickly estimate the total cost as $10 + $4 + $3 = $17. This gives you a good idea of how much money you will need without having to do exact calculations.
