Use rounding to check answers to calculations - Reasoning

Rosie attempted to verify her subtraction calculation using rounding to the nearest hundred as a strategy for estimation. Although rounding can be a useful tool for checking the plausibility of an answer, in this instance, Rosie's method led her to an incorrect conclusion. She rounded the numbers 12,456 and 4,528 to the nearest hundred, which gave her rounded figures of 12,500 and 4,500, respectively. Subtracting these rounded numbers, Rosie calculated an estimated answer of 8,000. However, the actual subtraction of the original numbers, 12,456 minus 4,528, equals 7,928, not the 7,000 she estimated. The discrepancy arises because the exact answer, when rounded to the nearest hundred, is 7,900, not 8,000. Therefore, Rosie's rounding approach caused her to overestimate the answer by 100.

It is important to understand why Rosie's use of rounding led to an incorrect estimate. When rounding both numbers down to the nearest hundred, the difference between the two rounded numbers became larger than the difference between the actual numbers. This is because the first number was slightly below the halfway mark to the next hundred, while the second number was slightly above the halfway mark to the lower hundred, amplifying the difference when rounded. This illustrates the potential pitfalls of using rounding for checking calculations, as it can sometimes give a misleading estimate, especially when the numbers fall near the rounding threshold. To avoid such errors, it's crucial to consider the direction and magnitude of the rounding applied to each number in the calculation.