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Chapter 1—Whole 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.

• Is 122 closer to 120 or to 130? It is closer to 120. So we can round 122 down to 120.

• Is 127 closer to 120 or to 130? It is closer to 130, so we can round 127 up to 130.

• Is 125 closer to 120 or to 130? It is right in the middle. By convention, however, we round upward when the value is exactly between the two choices. So we round 125 is rounded upward to 130.

 Procedure Step 1: Determine which digit is to be rounded This determines how accurate we want to make the estimated number. The number to be rounded is specified by its place value—to tens, hundreds, thousands, and so on. Step 2: Look at the digit immediately to the right of the rounding digit. If the digit immediately to the right of the rounding digit is less than 5, then do not change the rounding digit. If the digit immediately to the right of the rounding digit is 5 or greater, then increase the rounding digit by 1. Step 3: Change all digits to the right of the rounding digit to zero.

Example 1

 Problem Round 125,000 to the nearest ten-thousand. Procedure Determine which digit is to be rounded. 125,000 Look at the digit immediately to the right of the rounding digit. 125,000 This digit is equal to 5, so the rounding digit ( 2 ) is increased to 3. 135,000 Change all digits to the right of the rounding digit to zero. 130,000 Solution So 125,000 rounded to the nearest ten-thousand is 130,000

Examples and Exercises

 Use these interactive examples and exercises to strengthen your understanding and build your skills:

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