Chapter 1Whole Numbers
1-3 Rounding Whole Numbers
We often need to estimate values of whole numbers. Sometimes, for example, we say that there are 30 people in the class when, in fact there are 32. Numbers that are estimated are usually easier to work with and allow some "wiggle room" for accuracy. When it comes to estimating the number of people in a crowd, for instance, there is no point in trying to report exactly 1,234 people when and estimated value of 1,200 will suffice. So we commonly round off numbers when it is simpler, and actually more reasonable, to cite estimated values.
Here is the number line for whole numbers 50 through 60. This could represent the number of people in a room, cost of batteries for cell phones, or outdoor temperatures. We are given one of the values on the number line and need to round that value up to 60 or down to 50, depending upon which is closer.
If the given value is 53 and you want to round to the nearest tens place, you round down to 50. Why? Because 53 is clearly closer to 50 than to 60.
If the given value is 58 and you want to round to the nearest tens place, you round up to 60. Why? Because 58 is clearly closer to 60 then to 50.
But what if the given value is 55? It is no closer to 50 than to 60. It is directly in the middle. How do you round that value? By convention, when the given value is exactly in the middle of the range of values, always round up.
Values that are estimated in this way are said to be rounded or rounded off.
Examples and Exercises