Name:
Lesson 01 – Rational Numbers
Date:
Class:
Part A
1. Working with your partners, compare the following fractions by changing them to decimals.
Then group them into two different categories of your choosing.
1
2
4
7 5
2
11
9
2
;
;
;
;
;
;
;
;
4 3
9
8 11 15
12
20
25
Write a description for the two groups you choose. Include in your description why you choose
these two groups.
Part B
2. Read the following definitions, then complete the following activity.
A terminating decimal is a decimal that ends. It's a decimal with a finite number of digits.
A repeating decimal is a decimal that has a pattern that repeats infinitely.
Working with your partner roll two decahedron dice to create a fraction. The first roll will
represent the numerator, the second roll will represent the denominator. Write each fraction in
the applicable circle pictured below. Create 10 different fractions using the dice.
Exchange your papers with a different group. Have them check your work while you check their
work.
1
Lesson 01 – Rational Numbers
Part C
a
where a and b are integers an b  0.
b
Working with your partner, determine if the fractions you pulled out of your bag are rational
numbers. Explain your reasoning in the space provided below.
3. A rational number is a number that can be written as
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4. Henry and Jamar are trying to determine if 4 is a rational number. Henry says “ 4 is not a
fraction, so it’s not a rational number.” Jamar says, “I know how to write 4 as a fraction, so it is
a rational number.” Which student is correct? Explain your reasoning.
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5. Lisa and Christine are trying to determine if  0.15 is a rational number. Lisa says “  0.15 is a
decimal, not a fraction, so it’s not a rational number.” Christine says, “I know how to write
 0.15 as a fraction, so it is a rational number.” Which student is correct? Explain your
reasoning.
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Lesson 01 – Rational Numbers
2
to a decimal, his calculator screen read, “ 0.66666667" so
3
he assumed it was a terminating decimal. Write an explanation to Sam that will help him
2
understand why is actually a repeating decimal.
3
6. Sam used his calculator to change
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Early Finish:
7. Prove that the fraction
8. Prove that
1
is a repeating decimal. Show your work below.
7
9
is a terminating decimal.
17
Lesson 01 – Rational Numbers
Part D
Extra Practice
Identify which of the following numbers are terminating decimals and repeating decimals. Show
your work or explain your reasoning.
9.
11
30
10.
8
25
11.
12.
5
3
13.
9
50
14.
1
8
4
11
Prove that the following numbers are rational numbers.
15. 0.625
16. 1.02
17. 0.33