Sara estimated 23 x 43 using 20 x 40. Sam estimated 23 x 43 using 25 x 40. Whose method will give an estimate closer to the exact answer? Tell how you decided.
Sara rounded down both numbers.
Sam rounded one number down and the other up. It "evened" out more, his answer is closest to the exact one.
Well, let's take a closer look at their estimates. Sara estimated 23 x 43 by using 20 x 40, while Sam estimated it by using 25 x 40.
Now, since Sara's estimate is based on numbers that are smaller than the actual values, her estimated product will likely be smaller than the actual answer.
On the other hand, Sam's estimate is based on numbers that are larger than the actual values, so his estimated product will likely be larger than the actual answer.
So, if we compare their estimates to the actual answer, it seems like Sara's method using 20 x 40 will be closer to the exact answer. Although it is still just an estimate, Sara's method involved numbers that are closer to the actual values, giving her a better chance of getting a more accurate estimate.
To determine whose method will give an estimate closer to the exact answer, we can compare the two estimates to the actual answer and see which one is closer.
To find the actual answer of 23 x 43, we can calculate it:
23 x 43 = 989
Now let's compare the estimates.
Sara estimated 23 x 43 using 20 x 40:
20 x 40 = 800
The difference between Sara's estimate and the actual answer is:
|800 - 989| = 189
Sam estimated 23 x 43 using 25 x 40:
25 x 40 = 1000
The difference between Sam's estimate and the actual answer is:
|1000 - 989| = 11
Based on the differences, we can see that Sam's method will give an estimate closer to the exact answer. Sam's estimate is only off by 11, whereas Sara's estimate is off by 189.
To determine whose method will give an estimate closer to the exact answer, we need to compare the two estimates with the actual product of 23 x 43.
Sara estimated 23 x 43 using 20 x 40 = 800.
Sam estimated 23 x 43 using 25 x 40 = 1000.
To find the actual product of 23 x 43, we can either multiply the numbers directly or use a calculator.
23 x 43 = 989.
Now, we can calculate the differences between the estimates and the actual product:
For Sara's estimate: 989 - 800 = 189.
For Sam's estimate: 989 - 1000 = -11.
The absolute value of the difference indicates the distance between the estimate and the actual product. In this case, it represents how much the estimate deviates from the actual answer.
Comparing the differences, we see that Sara's estimate of 800 is 189 away from the exact answer, while Sam's estimate of 1000 is only 11 away.
Therefore, Sam's method will give an estimate that is closer to the exact answer, making it the more accurate estimation method in this case.