Estimation and Rounding

Rounding just asks a simple question — which tidy number is closest? That’s it. Let’s see what that looks like.

Round three thousand five hundred and eighty-three to the nearest thousand. The nearest thousands are three thousand and four thousand. Where does 3,583 sit between them? Over halfway across — closer to four thousand. So it rounds to four thousand.

Now round nine point three five to the nearest whole number. It sits between nine and ten, about a third of the way along — clearly closer to nine. An easy way to tell if we are closer to 9 or 10 is to look at the digit right after the nine. It’s a three. Three is less than five, so we’re closer to nine wholes than 10.

Here’s a tricky one. Round one hundred and twenty-three point five. That’s exactly halfway between 123 and 124. The convention is: if the next digit is five or more, we round up. So 123.5 rounds up to 124.

Let’s round to one decimal place. Round 1,512 point three-eight-two. We want one digit after the decimal, so we’re choosing between 1,512.3 and 1,512.4. Look at the next digit: it’s an eight. Eight is five or more, so we round up. The answer is 1,512.4.

Last one. A shopping trip. You grab three items: four dollars eighty-five, two nineteen, and nine forty-nine. We can quickly estimate the total by rounding each to the nearest dollar. Five plus two plus nine. About sixteen dollars. Now if we calculate exactly, the calculator shows sixteen point five three one. For everyday purposes we always round money to the nearest cent. So, to two decimal places, the actual charge is sixteen dollars and fifty-three cents.