Question

A yield percent of 82.6% is rounded to 83%. Explain why this is not correct.

a) Rounding up is always accurate
b) Rounding down is always accurate
c) Rounding to the nearest whole number may not be accurate in this case
d) Rounding to the nearest tenth is the best approach

Answer 1

The rounding of 82.6% to 83% is indeed correct since the first decimal place is 6, which requires rounding up to the nearest whole number. Scientific accuracy often demands not rounding off intermediate results and keeping more decimal places until the final calculation is made.

Step-by-step explanation:

The correct answer is (c) Rounding to the nearest whole number may not be accurate in this case. When we round a number to the nearest whole number, we look at the first decimal place. If this digit is 5 or greater, we round up. If it's less than 5, we round down. In this case, since the first decimal place is a 6, it's appropriate to round up from 82.6% to 83%.

However, scientific and mathematical precision sometimes demands more accurate rounding or maintaining more decimal places. Rounding errors can lead to inaccurate results, particularly in scientific work that requires a high level of detail or when performing a series of mathematical operations where intermediate results significantly impact the final answer. These situations prefer carrying intermediate results to more decimal places and only rounding the final answer.