Math 25 Activity 4: Rounding
When we work with decimals, many times we end up working with approximations of numbers
instead of working with the exact number. An example of needing exact numbers would be adding
or subtracting money because you are using dollars and cents. An example of approximation is
when we use  to help us calculate the area and circumference of a circle.
To be able to round, we need to know how to refer to the digits or place values of a numeral.
Review the following chart for a reminder of place values.
Various number systems have adopted different notations to indicate an infinite repeat of certain
digits. When written so that a number indicates an infinite repeat, the number is considered to be
written in exact form. For example, an exact form of the rational number 7 is 7 divided by 3. Using
3
long division, we end up with the quotient being 2 and the remainder being 1. Using decimals, we
could write it a couple of ways: 2.333... or 2. 3 or 2.(3) or 2.3 . In the rest of this activity, we will use
the vinculum, which is the bar over the repeated digits as in 2. 3 .
Typical Rounding, Rounding Up, or Rounding Down
Typical Rounding Rules: When rounding, typically you need a significant digit that you would like to
have a number in that place value, but no more digits to the right of it. The digit to the immediate
right of the significant digit is called the test digit. If the test digit is 4 or lower, then the test digit
and all digits to the right become 0. If the test digit is 5 or higher, then the significant digit goes up
by one, and then the test digits and all digits to the right become 0. We use the phrase “rounded
up” if the number got larger and we use the phrase “rounded down” if the number got smaller.
1. A common state’s sales tax is 7%. How much tax is on an item priced as $6.56?
2. Did you round to the nearest penny in question 1? What is your tax once you have rounded to the
nearest penny?
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The application problem you just solved is an example of typical rounding. You should have needed
to round up, because the test digit was a 9.
3. Can you think of any other examples where typical rounding applies?
Automatic Rounding Down: The next application is an example of rounding down. In some
applications, if the answer is not a whole number, then we round down because of the context.
4. A party planner needs a certain type of candy for gift bags which are sold in packs of 21.5 oz at
the store. The host wants 3.5 oz of candy in each gift bag. How many gift bags can be filled with one
pack of candy?
5. How many gift bags could she fill with 18 packs of candy?
6. Imagine the party planner took the answer from question 4 and multiplied by 18 to get the
answer to question 5. She thinks that 18 packs of candy will give her 108 gift bags. Imagine her
surprise when she had enough candy to fill two more gift bags than her calculated prediction! Write
a sentence explaining to her why she had some extra.
Problems where you could go over budget or where you need to give everyone the same amount
are examples where you need to round down.
Automatic Rounding Up: The next application demonstrates when we need to round up when the
answer is not a whole number.
7. A baker needs 133 pounds of flour for Monday’s bread order. He has 26 pounds in his inventory.
His vendor delivers 20 pound bags. How many bags of flour should he order from the vendor to be
able to complete Monday’s order?
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Instructor!
Work with your group to answer the following questions. Make sure to discuss the idea of rounding
up, down, picking a digit to round to using typical rounding, or leaving an answer exact. Your
instructor will write space for each question on the board and assign a couple of groups to each
question to write their answers up on the board. At the end, the class will discuss the answers and
correct any errors.
8. There are 54 children attending an outdoor education field trip. Answer the following:
Question
Exact calculated answer
Appropriate answer for the context
A. If six children fit in each car
with a chaperone, then how
many cars need to be rented
based on children attending?
B. If ten children can sleep in a
tent, then without considering
the chaperones, how many
tents do you need for the
children?
C. If you only have $2250 to pay
for the children’s food during
the trip, then how much money
should you budget per child
using as much as you can for
each child while not exceeding
your overall budget?
D. If you had a donation of 200
disposable cameras for the
students to use to document
nature during the trip, then
how many should each child
receive?
E. If you bought a set of
flashlights to use on the trip for
$138.56, then how much sales
tax will be added to your
purchase if the state tax is 7%?
9. Did you include units in your answers in question 8? If no, then go back and write appropriate
units on each answer.
Why are units important in application problems?
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10. Review typical rounding rules on the following examples, then write “rounded up” or “rounded
down.”
Example
Round to the
nearest whole
Round to the
nearest tenth
Round to the nearest
hundredth
Round to the nearest
thousandth
2.5646
59.9849
36.0005
82.4467
689.9876
11. Summary: First, discuss these examples in your group, then try to come up with two more
examples for each type of rounding. Your instructor will leave space on the board to list examples of
typical rounding, automatic rounding up, and automatic rounding down.
Typical Rounding: leaving a tip, calculating sales tax, grade on a test
Automatic Rounding Up: buying cans of paint for a room, ordering invitations, lodging for guests,
seats in cars
Automatic Rounding Down: age, ordering wedding cake for guests at a reception
Instructor!
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