Rounding Off
Rounding Off
Rounding off a decimal number to a given number of decimal places is the quickest way to approximate a number. For example, if you wanted to round off \(\text{2.6525272}\) to three decimal places, you would:
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count three places after the decimal and place a \(|\) between the third and fourth numbers;
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round up the third digit if the fourth digit is greater than or equal to \(\text{5}\);
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leave the third digit unchanged if the fourth digit is less than \(\text{5}\);
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if the third digit is \(\text{9}\) and needs to be rounded up, then the \(\text{9}\) becomes a \(\text{0}\) and the second digit is rounded up.
So, since the first digit after the \(|\) is a \(\text{5.}\) we must round up the digit in the third decimal place to a \(\text{3}\) and the final answer of \(\text{2.6525272}\) rounded to three decimal places is \(\text{2.653}\).
The following video explains how to round off.
Example
Question
Round off the following numbers to the indicated number of decimal places:
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\(\dfrac{120}{99}=\text{1.}\dot{1}\dot{2}\) to \(\text{3}\) decimal places.
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\(\pi =\text{3.141592653...}\) to \(\text{4}\) decimal places.
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\(\sqrt{3}=\text{1.7320508...}\) to \(\text{4}\) decimal places.
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\(\text{2.78974526}\) to \(\text{3}\) decimal places.
Mark off the required number of decimal places
If the number is not a decimal you first need to write the number as a decimal.
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\(\dfrac{120}{99} = \text{1.212}|121212\ldots\)
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\(\pi =\text{3.1415}|92653\ldots\)
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\(\sqrt{3}=\text{1.7320}|508\ldots\)
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\(\text{2.789}|74526\)
Check the next digit to see if you must round up or round down
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The last digit of \(\cfrac{120}{99}=\text{1.212}|121212\dot{1}\dot{2}\) must be rounded down.
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The last digit of \(\pi =\text{3.1415}|92653\ldots\) must be rounded up.
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The last digit of \(\sqrt{3}=\text{1.7320}|508\ldots\) must be rounded up.
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The last digit of \(\text{2.789}|74526\) must be rounded up.
Since this is a \(\text{9}\) we replace it with a \(\text{0}\) and round up the second last digit.
Write the final answer
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\(\dfrac{120}{99}=\text{1.212}\) rounded to \(\text{3}\) decimal places.
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\(\pi =\text{3.1416}\) rounded to \(\text{4}\) decimal places.
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\(\sqrt{3}=\text{1.7321}\) rounded to \(\text{4}\) decimal places.
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\(\text{2.790}\)
This lesson is part of:
Algebraic Expressions Overview