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Chapter 1—Whole Numbers 1-3 Rounding Whole Numbers
When you complete the work for this section, you should be able to: - Demonstrate how to round whole-number values to a given place value.
| 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. 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 The Problem: Round 6,734 to the nearest hundred. Step 1: Determine which digit is to be rounded. 6,734 Step 2: Look at the digit immediately to the right of the rounding digit. 6,734 This digit is less than 5, so the rounding digit ( 7) remains unchanged. Step 3: Change all digits to the right of the rounding digit to zero. 6,700 The Solution: So 6,734 rounded to the nearest hundred is 6,700. Example 2 The Problem: Round 13,874 to the nearest thousand. Step 1: Determine which digit is to be rounded. 13,874 Step 2: Look at the digit immediately to the right of the rounding digit. 13,874 This digit is greater than 5, so the rounding digit ( 3 ) is increased to 4. 14,874 Step 3: Change all digits to the right of the rounding digit to zero. 14,000 The Solution: So 13,874 rounded to the nearest thousandth is 14,000. Example 3 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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