The Neighbour Decides

Rounding can make a long number feel simple in seconds. But one tiny digit controls the whole decision... and it is NOT the digit you are rounding. That makes rounding a quick detective puzzle: mark the place, then question its neighbour.

First, find the stated place. Suppose you round 6,472 to the nearest hundred. The hundreds digit is four. Its place value is four hundred, not simply four. Mark that digit, because it is the one that may stay or rise. You do not round every digit in turn. Now look exactly one place to the right. Here, the tens digit is seven. This is the deciding digit. Zero, one, two, three or four means round down. Five, six, seven, eight or nine means round up. Picture 6,472 between 6,400 and 6,500. The halfway point is 6,450. Because 6,472 lies beyond halfway, it is closer to 6,500. That is why the adjacent seven tells the hundreds digit to rise. Four hundreds becomes five hundreds. Every digit to the right becomes zero, giving 6,500. Digits further right do not get separate votes; only the neighbour beside the marked place decides.

Let's work through an example. A question asks: round 38.746 to the nearest tenth. The stated place is tenths, so find the first digit after the decimal point. That digit is seven, worth seven tenths. Highlight it. Look one place right, at the hundredths digit. It is four. Four is below five, so round down. The seven stays seven. Remove the later digits, but keep the decimal point to show the tenths place clearly. So 38.746 rounded to the nearest tenth is 38.7. Notice that the six in the thousandths place cannot change the decision. It is not next door to the rounding digit. The four has already decided it.

Find the place, check its neighbour on the right, then keep or raise the marked digit and tidy what follows. You can round any number confidently... one careful glance decides it!