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Problem Set Solutions
0.04
3.3125
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Example 1: Can All Rational Numbers Be Written as Decimals?
a. Using the division button on your calculator, explore various quotients of integers 1 through 11.
Record your fraction representations and their corresponding decimal representations in the
space below.
b. What two types of decimals do you see?
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Example 2: Decimal Representations of Rational Numbers
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In the chart below, organize the fractions and their corresponding decimal representations listed in
example 1 according to their type of decimal.
Terminating Non-Terminating
What do these fractions have in common? What do these fractions have in common?
The denominators
are only divisible by
factors of 2's and
5's.
The denominators
are only divisible by
another factor other
than factors of 2's
and 5's.
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Example 3: Converting Rational Numbers to Decimals Using Long-Division
Use the long division algorithm to find the decimal value of
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Exercise 1:
Convert each rational number to its decimal form using long division
a.
b.
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Example 4: Converting Rational Numbers to Decimals Using Long-Division
Use long division to find the decimal representation of
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Question:
What part of your calculation causes the decimal to repeat?
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Exercise 2
Calculate the decimal value of the fraction below using long division. Express your answers using
bars over the shortest sequence of repeating digits.
a. b.
c. d.
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Exercise 2
Calculate the decimal value of the fraction below using long division. Express your answers using
bars over the shortest sequence of repeating digits.
a. b.
c. d.
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Example 5: Fractions Represent Terminating or Repeating Decimals
How do we determine whether the decimal representation of a quotient of two integers, with the
divisor not equal to zero, will terminate or repeat?
If the remainder is zero:
If the remainder is not zero:
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Example 6: Using Rational Number Conversions in Problem Solving
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a. Eric and four of his friends are taking a trip across the New York State Thruway. They
decide to split the cost of tolls equally. If the total cost of tolls is $8, how much will each
person have to pay?
b. Just before leaving on the trip, two of Eric's friends have a family emergency and cannot
go. What is each person's share of the $8 toll now?
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Closing:
1.) What should you do if the remainders
of a quotient of integers do not seem to
repeat?
2.) What is the form for writing a
repeating decimal?
