What Is the Difference Between Rounding & Estimating?

Rounding

Numbers are rounded up or down when they are more precise than is required, making them awkward to deal with. For instance, a population of 148536 can be rounded up to the nearest 10000 for most purposes and written as 150000. Some numbers have to be rounded up or down, as they are infinitely long in their written form. For example, 1/3 written as a decimal is 0.333 recurring, meaning there are an infinite number of threes. Therefore the number is rounded down to two or three decimal places. If the place, or decimal place, the number is rounded up or down to is 5 or over, the number is rounded up; otherwise, it is rounded down.

Estimating is an calculated approximation, taking into account already known figures or previously known facts. For example, Fred sees a garden shed he wants to buy, but doesn't know the size. He thinks, however, it is roughly twice the size of his current shed, so he can double the dimensions of his own shed as an estimation.

Rounding and estimating are different in that estimations come up with new numbers altogether, while rounding slightly adjusts an already existing number. Estimations are likely to be done quickly in our head, purely for our own benefit. The number reached could be different every time. Rounding, on the other hand, will always result in the same number once we know what place, or decimal place, the number needs to be rounded up or down to. You should never assume a number should be rounded up or down, just follow instructions to do so. Exceptions to this are recurring numbers and, when calculating monetary values, fractions of a cent should be rounded up or down.

Rounded numbers are regularly used during estimations. The imprecise nature of rounded numbers is what estimating is all about -- a rough calculation. For example, Fred knows his current garden shed is 3.58 meters long. For his estimation of the size of the new shed, he doubles 3.60 and guesses it is 7.20 meters long, which he rounds down to 7 meters in his head. As he isn't measuring anything precisely, it might be 7 meters long anyway, or 7.20 meters, but it doesn't matter. To know it is roughly 7 meters long is enough for him.