Several methods are used for rounding a number to a selected decimal position. One method is called truncation
. A decimal is said to be truncated, when only the front few decimal places are used, i.e. all digits after a selected place value are dropped. A second method is rounding to the nearest selected place-value. A third method is to round up to a selected place value.
Examples: Consider the repeating decimal fraction 0.6666… where the selected position is the hundredths.
The rounded value using truncation would be 0.66.
The rounded value to the nearest hundredth is 0.67.
The rounded value using round up would be 0.67.
The type of rounding to be used and the position to round to should be determined by the application problem being solved.
Examples: Consider the following three problems.
A wagon has a maximum capacity of 119 pounds. How many 12 pound bricks can be loaded into the wagon?
119 ÷ 12 = 9.916666… Since adding too much weight could break the wagon, we would truncate. So, the solution is 9 bricks.
What is the mean amount earned by 12 students who earned a total of $119?
119 ÷ 12 = 9.916666… We would probably round this to the nearest cent since we are finding the mean. So, the solution is $9.92.
How many ceramic tile are needed for a 121 inch frieze if each tile measures 12 inches by 12 inches?
121 ÷ 12 = 10.083333… Since we would want to purchase enough tile to complete the frieze pattern, we would need to round up. So, the solution is 11 tiles.
Calculators either round to the nearest or truncate because they can only display so many decimal places on the screen. You would either need to read the instruction manual or test with a sample problem the method used by any particular calculator. Students are often not aware that the value seen on the display is not the actual value, but is a rounded approximation.
Students often want to get around the difficulty presented by repeating decimals (and very long strings of decimal digits) by using just a few decimal places by rounding the decimal. Often this gives a very close approximation for the actual arithmetic answer. But it is important to label the solution as an approximation. DO NOT USE AN EQUALS SIGN when you have rounded or truncated a decimal value in arithmetic.
Also, there are some cases in which rounding or truncating will result in a large difference in the answers to the arithmetic. For instance, what is the difference between earning 5.5% interest on $80,000 over 30 years and earning 5.51% interest on $80,000 over 30 years? Each of these percentage rates rounds to 5.5%, but the difference in what you receive at the end of 30 years is $1135.34, which means the extra 0.1% is quite a bit more money.
Unhappy father to daughter who has come home at 3:00 a.m.
Father: "I told you to be home by a quarter of twelve!"
Daughter: "But I learned in math class that a one-fourth of twelve is three."
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Date last modified: June 30, 2010.
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By Kris Montis and Timothy Peil
