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1.2 E) Estimating Calculations – Part 2
1.2 E) Estimating Calculations – Part 2
The content in this section builds on the content that was discussed in the previous section. Therefore, make sure that you have covered the content in the previous section first before working through the content in this section.
Example 1
We are now going to have a look at an example of an estimation calculation that involves division.
We have the calculation below.
We are now going to have a look at an example of an estimation calculation that involves division.
We have the calculation below.
a) By rounding each of the numbers involved to 1 significant figure, find an estimate for the calculation above.
b) Is your answer an under or overestimate?
Part a
The first step in answering this question is to round both of the numbers involved to one significant figure. When rounded to one significant figure, the numerator of the fraction becomes 30,000 and the denominator becomes 600. Therefore, the rounded calculation becomes what is given below.
b) Is your answer an under or overestimate?
Part a
The first step in answering this question is to round both of the numbers involved to one significant figure. When rounded to one significant figure, the numerator of the fraction becomes 30,000 and the denominator becomes 600. Therefore, the rounded calculation becomes what is given below.
The next step is to undertake the calculation.
Therefore, our estimate is 50.
Part b
The second part of the question asks us whether our estimate is an under or overestimate. In order to find out whether our answer is an under or overestimate, we need to look at the rounding direction that the numbers moved in. We rounded our numerator up and our denominator down. This meant that we were dividing a larger number by a smaller number, and this will result in the estimated answer being greater than the actual answer. Therefore, our estimate is an overestimate.
The actual answer for this calculation is 41.336939… and our estimate was 50.
Part b
The second part of the question asks us whether our estimate is an under or overestimate. In order to find out whether our answer is an under or overestimate, we need to look at the rounding direction that the numbers moved in. We rounded our numerator up and our denominator down. This meant that we were dividing a larger number by a smaller number, and this will result in the estimated answer being greater than the actual answer. Therefore, our estimate is an overestimate.
The actual answer for this calculation is 41.336939… and our estimate was 50.
Division – Under or Overestimate
Here are the rules for under and overestimate for division.
If we are rounding the numerator up and the denominator down, we will have an estimate that is an overestimate. This is because in our estimate calculation, we will be dividing a larger number (the numerator) by a smaller number (the denominator), which will result in the estimated answer being greater than the actual answer, thus meaning that the estimate will be an overestimate.
Here are the rules for under and overestimate for division.
If we are rounding the numerator up and the denominator down, we will have an estimate that is an overestimate. This is because in our estimate calculation, we will be dividing a larger number (the numerator) by a smaller number (the denominator), which will result in the estimated answer being greater than the actual answer, thus meaning that the estimate will be an overestimate.
If we are rounding the numerator down and the denominator up, we will have an estimate that is an underestimate. This is because in our estimate calculation, we will be dividing a smaller number (the numerator) by a larger number (the denominator), which will result in the estimated answer being less than the actual answer, thus meaning that the answer will be an underestimate.
If the numerator is rounded in one direction and the denominator is rounded in the same direction, we will not be able to say whether the estimate is an under or overestimate.
It is worth getting the rules regarding multiplication or division and under or overestimate from this section and the previous section down on a revision card.
It is worth getting the rules regarding multiplication or division and under or overestimate from this section and the previous section down on a revision card.
Example 2
Sometimes we will be given an estimation calculation where there are many different components. We answer these questions in the same way as the other questions. We round each of the numbers to one significant figure and then we complete the calculation.
Find an estimate for the calculation below by rounding each number to 1 significant figure.
Sometimes we will be given an estimation calculation where there are many different components. We answer these questions in the same way as the other questions. We round each of the numbers to one significant figure and then we complete the calculation.
Find an estimate for the calculation below by rounding each number to 1 significant figure.
The first step in answering this question is to round each of the numbers in the calculation to 1 significant figure. The 305 will be rounded down to 300, the 29 will be rounded up to 30 and the 8.759 will be rounded up to 9. The calculation with the rounded numbers becomes.
We are now able to complete the calculation.
A rough estimate for this calculation is 30.