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Study Guides > Mathematics for the Liberal Arts Corequisite

Rounding Decimals

Learning Outcomes

  • Round a decimal to a given place value
In the United States, gasoline prices are usually written with the decimal part as thousandths of a dollar. For example, a gas station might post the price of unleaded gas at $3.279\$3.279 per gallon. But if you were to buy exactly one gallon of gas at this price, you would pay $3.28 , because the final price would be rounded to the nearest cent. In a lesson about whole numbers, we learned that we can round numbers to get an approximate value when the exact value is not needed. Suppose we wanted to round $2.72 to the nearest dollar. Is it closer to $2 or to $3? What if we wanted to round $2.72 to the nearest ten cents; is it closer to $2.70 or to $2.80? The number lines in the image below can help us answer those questions. (a) We see that 2.722.72 is closer to 33 than to 22. So, 2.722.72 rounded to the nearest whole number is 33. (b) We see that 2.722.72 is closer to 2.702.70 than 2.802.80. So we say that 2.722.72 rounded to the nearest tenth is 2.72.7. In part a, a number line is shown with 2, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9 and 3. There is a dot between 2.7 and 2.8 labeled as 2.72. In part b, a number line is shown with 2.70, 2.71, 2.72, 2.73, 2.74, 2.75, 2.76, 2.77, 2.78, 2.79, and 2.80. There is a dot at 2.72. Can we round decimals without number lines? Yes! We use a method based on the one we used to round whole numbers.

Round a decimal.

  1. Locate the given place value and mark it with an arrow.
  2. Underline the digit to the right of the given place value.
  3. Is this digit greater than or equal to 5?5?
    • Yes - add 11 to the digit in the given place value.
    • No - do not change the digit in the given place value
  4. Rewrite the number, removing all digits to the right of the given place value.
  Tip:  If the digit to the right of your given place value is 5 or above, give your given place value a shove.  If the digit to the right of your given place value is 4 or less, let your given place value rest.  

example

Round 18.37918.379 to the nearest hundredth. Solution
18.37918.379
Locate the hundredths place and mark it with an arrow. .
Underline the digit to the right of the 77. .
Because 99 is greater than or equal to 55, add 11 to the 77. .
Rewrite the number, deleting all digits to the right of the hundredths place. 18.3818.38
18.3818.38 is 18.37918.379 rounded to the nearest hundredth.
 

try it

[ohm_question]146242[/ohm_question]
 

example

Round 18.37918.379 to the nearest
  1. tenth
  2. whole number

    Answer:

Solution
1. Round 18.37918.379 to the nearest tenth.
18.37918.379
Locate the tenths place and mark it with an arrow. .
Underline the digit to the right of the tenths digit. .
Because 77 is greater than or equal to 55, add 11 to the 33. .
Rewrite the number, deleting all digits to the right of the tenths place. 18.418.4
So, 18.37918.379 rounded to the nearest tenth is 18.418.4.
2. Round 18.37918.379 to the nearest whole number.
18.37918.379
Locate the ones place and mark it with an arrow. .
Underline the digit to the right of the ones place. .
Since 33 is not greater than or equal to 55, do not add 11 to the 88. .
Rewrite the number, deleting all digits to the right of the ones place. 1818
So 18.37918.379 rounded to the nearest whole number is 1818.

 

try it

[ohm_question]146244[/ohm_question]
Watch the following video to see an example of how to round a number to several different place values. https://youtu.be/qu4Y9DGqXlk

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