# Rounding

When an approximate value for a measurement, or other number, is needed, rounding can be used. For example, a person might say that he or she owns 100 books when the actual number of books that person owns might be 98 or 104. Sometimes the process of giving an approximate number is also called rounding off.

Suppose a measurement of 15.42 inches needs to be rounded to the nearest inch. The first step is to ask this question: "Is 15.42 inches closer to 15 inches or to 16 inches?" Because 15.42 is closer to 15 inches, 15.42 rounds to 15. Similarly, a measurement of 15.62 inches would be rounded to 16.

But what about a measurement of 15.5 inches? This measurement is exactly halfway between 15 and 16 inches. There are two ways to solve this dilemma. The first way, which is the most often used, is to round up when the digit is 5. Thus 15.5 rounds to 16. But what about 15.55? This is not midway between 15 and 16 because 15.55 is closer to 16 than to 15. So, when rounding, one should consider all the digits to the right of the place to which the number is being rounded (in this case, the units place).

The second way to round when the number is midway is often used in scientific calculation. To see how this works, consider these 4 measurements:7.5, 4.5, 6.5, and 8.5. If one rounds all four measurements to the nearest inch, the result is 8, 5, 7, and 9, but this way of rounding may build in error. If the original measurements are added, the total is 27 inches. Compare this to the total for the rounded numbers, 29. Rounding created an error equal to 2 inches.

If, however, one rounds by the second, or scientific, method, the following rule is applied: Round when the number is midway so that the result is always an even number. What values will this give for the 4 numbers in the previous example? The result is 8, 4, 6, and 8. The total of these is 26, which is only 1 inch from the total of the original measurement. Rounding in this way tends, in the long run, to balance out the rounding errors because in a long list of numbers to be rounded, of those that are midway, about half will be even and half will be odd.

Sometimes the context of a problem will indicate which way to round a number properly. For example, in a survey taken to find how many pets live in a neighborhood, it is found that 7 neighbors have a total of 24 pets. Does this mean that the neighbors have , or , pets each? It may be better to report that each neighbor has an average of about 3 pets each, although the actual calculation results in a fraction of a pet.

see also Estimation; Significant Figures or Digits.

Lucia McKay

## Bibliography

Pappas, Theoni. The Joy of Mathematics: Discovering Mathematics All Around You. San Carlos, CA: World Wide Publishing, 1989.

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