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Math: Basic Tutorials : Decimals and Rounding
Decimals and Rounding
Decimal numbers show values that are less than a whole number by placing them after a decimal point (e.g. 0.2). The value of a number depends on where it is in relation to the decimal point. Sometimes, the result of an expression may have a long string of numbers after the decimal point, but you may need to make that answer shorter. This is called rounding. This section explains place value and how you can round decimal numbers.
Examples and Activity
| Example 1. Round 21.6573 to the indicated place value. | ||
|---|---|---|
| Tenths: | 21 decimal 6 5 7 3 rounded to the nearest tenth is 21 decimal 7 | The 6 is the tenths place. To round to the nearest tenth, we have to look at the number to the right of the 6. Because the number to the right of the 6 is greater than or equal to five, we round the 6 up to a 7 and remove the remaining digits. |
| Hundredths: | 21 decimal 6 5 7 3 rounded to the nearest hundredth is 21 decimal 6 6 | The 5 is in the hundredths place. To round to the nearest hundredth, we have to look at the number to the right of the 5. Because the number to the right of the 5 is greater than or equal to five, we round the 5 up to a 6 and remove the remaining digits. |
| Thousandths: | 21 decimal 6 5 7 3 rounded to the nearest thousandth is 21 decimal 6 5 7 | The 7 is in the thousandths place. To round to the nearest thousandth, we have to look at the number to the right of the 7. Because the number to the right of the 7 is less than five, we keep the 7 in the thousandths place and remove the remaining digits. |
| Ones: | 21 decimal 6 5 7 3 rounded to the nearest one is 22 | The 1 is in the ones place. To round to the nearest one, we look at the number to the right of the 1. Because the number to the right of the 1 is greater than or equal to five, we round the 1 up to a 2 and remove the remaining digits. |
| Tens: | 21 decimal 6 5 7 3 rounded to the nearest ten is 20 | The 2 is in the tens place. To round to the nearest ten, we look at the number to the right of the 2. Because the number to the right of the 2 is less than five, we keep the 2, replace the ones value with zero, and remove the remaining digits. |
Example 2. Place Value of Whole Numbers and Decimals: Based on where they appear in the number, what is the value of each digit? Click on question marks to see the place value of each digit.
Example 2. Rounding of Whole Numbers and Decimals: What would the number below be if we rounded it to the nearest thousands? Nearest hundred thousands? Nearest millions? Click on the question marks to see the value of this number rounded to the place value of each digit.
Test Your Knowledge: Try this activity to test your skills. If you have trouble, check out the information in the module for help.
Place Value Quiz
Summary and Worksheet
- Summary: Decimals, Rounding, and Place Value - PDF - Opens in a new windowThis document contains a short (1 – 2 page) summary of this topic as well as detailed examples to illustrate key concepts. Use this summary to review this topic.
- Worksheet: Place Value and Rounding - PDF - Opens in a new windowThis document contains practice questions on this topic. Use the worksheet to test your knowledge and practice the skills learned in this module. The answers to the practice questions are provided at the end.