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Chapter 1 Whole Numbers 1-3 Rounding Whole Numbers - Is 168 closer to 160 or 170? It is closer to 170, of course. So we can say that 168 is about the same as 170.
- Is 162 closer to 160 or to 170. It is closer to 160. So we can say that 162 is about the same as 160.
- But what about 165? Is it closer to 160 or 170? Nether--it is exactly in the middle. In that case, we simply remember to "round up" to 170.
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. Vaules that are estimated in this way are said to be rounded or rounded off. Consider these questions: - 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.
Exercises 1. Is 44 closer to 40 or to 50? | 2. Is 66 closer to 60 or to 70? | 3. Is 75 closer to 70 or to 80? | 4. Is 367 closer to 370 or to 360 | 5. Is 13,278 closer to 13,000 or to 14,000 | | Ans. 1. 40 2. 70 3. It is in the middle, but rounded upward to 80 by convention. 4. 370 5. 13,000 The first step in rounding a number is to determine which digit is to be rounded--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. Examples 1. Round 6,734 to the nearest hundred. In this example, the 7 is in the hundreds place ( 6,734 ). So is this number closer to 6,700 or to 6,800? The digit immediately to the right of the 7 is less than 5; so the value should be rounded down from 6,734 to 6,700. 2. Round 14,874 to the nearest thousand. The question is this: Is 14,874 closer to 14,000 or to 15,000? Do we round the number down to 14-thousand or up to 15-thousand? The digit immediately to the right of the rounding digit is 8. This means the number is rounded upward to 15,000. 3. Round 125,000 to the nearest ten-thousand. Working with the ten-thousand place, the question is whether 125,000 is closer to 120,000 or 130,000. The digit immediately to the right of the ten-thousands place is a 5. That puts the number exactly half-way between 120,000 and 130,000; so it should be rounded up to 130,000
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