Estimate the difference of 645 and 273.
Answer (2)
Round 645 and 273 to the nearest ten: 650 and 270.
Calculate the difference: 650 − 270 = 380 .
The estimated difference is 380 .
Explanation
Problem Analysis We are asked to estimate the difference between 645 and 273. There are several ways to estimate, such as rounding to the nearest hundred or the nearest ten. Let's explore both methods to see which gives a reasonable estimate.
Rounding to Nearest Hundred First, let's round both numbers to the nearest hundred. 645 rounded to the nearest hundred is 600. 273 rounded to the nearest hundred is 300.
Calculating the Difference (Hundreds) Now, calculate the difference between the rounded numbers: 600 − 300 = 300
Rounding to Nearest Ten Next, let's round both numbers to the nearest ten. 645 rounded to the nearest ten is 650. 273 rounded to the nearest ten is 270.
Calculating the Difference (Tens) Now, calculate the difference between the rounded numbers: 650 − 270 = 380
Comparing Estimates The actual difference between 645 and 273 is: 645 − 273 = 372 Rounding to the nearest ten gives us an estimate of 380, which is closer to the actual difference than rounding to the nearest hundred, which gives us an estimate of 300.
Final Answer Therefore, a good estimate of the difference between 645 and 273 is 380 .
Examples
Estimating differences is useful in everyday situations, such as when you're shopping and want to quickly calculate the approximate change you'll receive. For example, if you buy items costing $645 and pay with $1000, you can quickly estimate your change by rounding $645 to $650. Then, you subtract $650 from $1000 to get $350, giving you a rough idea of the change you should expect. This helps you verify if the cashier gives you the correct amount back.
To estimate the difference between 645 and 273, we round 645 to 650 and 273 to 270, giving us an estimated difference of 380. Rounding to the nearest hundred gives a larger estimate of 300, which is further from the actual difference. Thus, 380 is a more accurate estimation using rounding to the nearest ten.
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