The concept of "rounding" means to make a number simpler, but keeping the number close to its original value. Rounding always yields a less accurate value.
Rounding is an approximation.
 The most common method of rounding is called "Half Round Up".
This is the method of rounding which makes "0.5 go up". Example: 3.5 rounds up to 4. |
There are many different methods for rounding numbers. The most "commonly used" method is the one stated above. This will also be the method used on this web site.
Steps in Rounding:
• Decide to which place value you will be rounding. Focus on that location.
• Leave that place value the same if the next digit is less than 5.
• Or, increase that place value by one if the next digit is 5 or more.
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Rounding Whole Numbers: tens, hundreds, thousands, etc.
Example: Round 48 to nearest ten.
Solution: Focus on the place value of "4" (it is the 10s position).
The next digit is "8", which is 5 or more, so increase the 10s value by 1.
ANSWER: 50 (48 is closer to 50 than to 40)
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• Round 32 to the nearest ten, gives 30. (32 is closer to 30 than to 40).
• Round 45 to the nearest ten, gives 50. (By half round up, 45 is closer to 50).
• Round 136 to the nearest ten, gives 140. (136 is closer to 140 than to 130).
• Round 136 to the nearest hundred, gives 100 (focus on 1, next digit < 5, leave 1)
• Round 24,656 to the nearest thousand,
gives 25,000 (focus on 4, next digit >5, add 1)
Rounding decimals: tenths, hundredths, thousandths, etc.
Example: Round 1.7321 to nearest tenths.
Solution: Focus on the place value of "7" (it is the 10ths position).
The next digit is "3", which is less than 5, so leave the 7.
ANSWER: 1.7 |
• Round 1.73212 to the nearest hundredths, gives 1.73 (number after 3 is < 5, so leave 3).
• Round 1.7321 to the nearest thousandths, gives 1.732 (number after 2 is < 5, so leave 2).
• Round 13.5 to the nearest integer, gives 14 (focus on 3, next digit =5, half round up)
Note: This example could also have asked you to round to the nearest whole number and the answer would be the same.
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A wavy equal sign may indicate that a rounding has occurred.
The symbol means "approximately equal to".
Example:  |
How do you round negative numbers?
As you can probably guess, there are many different methods for rounding negative numbers. The method stated below is a "commonly used" method, and will be the method used on this web site.
There is a process, referred to as "rounding away from zero" that can employ the concept of "Half Round Up", and can be applied to both positive and negative values.
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When rounding away from zero,
the values of 5 or more,
indicate rounding to the next number away from zero.
8.65 rounded to nearest tenth is 8.7 (going away from zero to the right)
-8.65 rounded to nearest tenth is -8.7 (going away from zero to the left)
This method is in keeping with the
concept of "opposites"
between positive and negative integer values.
You can also think of this method as
"take the absolute value of the negative value,
round that value,
then restore the sign".
-8.65 rounded to nearest tenth is | -8.65 | = 8.65 ≈ 8.7 restore to -8.7
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