Question

a. Estimate the sum: \(171+90+226\) b. Determine the actual sum. c. Was your estimate higher, lower, or the same as the actual sum?

Short answer

The estimated sum is 490, the actual sum is 487; the estimate is slightly higher.

Step-by-step solution

Estimating the Sum

To estimate the sum of the numbers, we round each number to the nearest ten. The number 171 rounds to 170, 90 remains 90, and 226 rounds to 230. Adding these estimates together gives us: \(170 + 90 + 230 = 490\)

Calculating the Actual Sum

Now calculate the actual sum of the original numbers: \(171 + 90 + 226 = 487\)

Comparing Estimates to Actual

Compare the estimated sum to the actual sum. Our estimate was 490 and the actual sum is 487. Hence, the estimate of 490 is slightly higher than the actual sum of 487.

Key concepts

Rounding Numbers

Rounding numbers helps in simplifying calculations by adjusting each number to a more manageable value. To round a number to the nearest ten, you identify which two multiples of ten it falls between. Then, decide which of these multiples it is closer to. For instance:

• The number 171 falls between 170 and 180. Since it is closer to 170, we round down to 170.
• The number 90 is already a multiple of ten, so it remains 90.
• The number 226 lies between 220 and 230. Since it is closer to 230, we round up to 230.

These rounded numbers are then used in further calculations such as estimating sums, leading to easier arithmetic.

Addition

Addition is the process of finding the total when two or more numbers are combined. When we add numbers like 171, 90, and 226, we are calculating their sum. This operation can be straightforward or a bit more complex depending on the numbers involved.Adding estimated values helps us quickly determine an approximate total. For instance, using our rounded numbers from before, we estimate: \[170 + 90 + 230 = 490\].On the other hand, calculating the exact sum of the original numbers yields:\[171 + 90 + 226 = 487\].While estimates provide quick approximations, actual addition results in precise totals, which is necessary when exactness is crucial.

Comparing Estimates

Comparing estimates to actual sums involves looking at both the rounded and exact calculations to determine any discrepancies between them. This process can provide insight into the accuracy of estimations. In the example of estimating and calculating the sum of 171, 90, and 226:

• The estimate was 490.
• The actual sum was 487.

Here, the estimated sum was higher than the actual sum by a small margin. These comparisons help us understand how rounding and estimation can influence the accuracy, often being slightly higher or lower than precise calculations. Understanding this relationship is crucial in checking whether estimates are close enough for practical purposes.