LESSON Rational and Irrational Numbers 1-1 Reteach
Name ________________________________________ Date __________________ Class __________________
LESSON
1-1
Rational and Irrational Numbers
Reteach
To write a fraction as a decimal, divide the numerator by the denominator.
A decimal may repeat.
0.3
1
= 3 1.00
3
?9 ¡ý
10
?9
1
A decimal may terminate.
0.75
3
= 4 3.00
4
?28¡ý
20
?20
0
Complete to write each fraction as a decimal.
1.
15
= 4 15.00
4
2.
5
= 6 5.00
6
3.
11
= 3 11.00
3
Every positive number has two square roots, one positive and one negative.
Since 5 ¡Á 5 = 25 and also ?5 ¡Á ?5 = 25,
both 5 and ?5 are square roots of 25.
25 = 5 and ? 25 = ?5
Every positive number has one cube root.
Since 4 ¡Á 4 ¡Á 4 = 64, 4 is the cube root of 64.
Find the two square roots for each number.
4. 81
________________________
5. 49
6.
________________________
25
36
________________________
Find the cube root for each number.
7. 27
________________________
8. 125
9. 729
________________________
________________________
Original content Copyright ? by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
4
9.
Success for English Learners
5
5
,?
2
2
1.
10. 7
2. Possible answer: If you have a square
with a side length of 5, then 52 is how
you find the area of that square.
11. 1
12.
1
= 0.25
4
2
3
3. Because the answer is an
approximation.
13. 5.66
14. 7.68
LESSON 1-2
15. 10.86
Practice and Problem Solving: A/B
16. 0.17 mi2
1. real, rational
17. 5 ft
2. real, irrational
Reteach
3. real, rational, integer
1. 3.75
4. real, rational, integer
2. 0.83
5. real, rational
3. 3.6
6. real, rational, integer, whole
4. 9, ?9
7. false; irrational real numbers include
nonterminating decimals
5. 7, ?7
6.
8. true; whole numbers are nonnegative
integers.
5 5
,?
6 6
9. rational; all money amounts can be
written as fractions
7. 3
8. 5
10. real numbers; the temperature can be
any number between 0 and 100 degrees
Celsius
9. 9
Reading Strategies
11. rational, real
1. Yes, because it can be written as a
fraction: 0.62 = 62 = 31 .
100
50
12. integers, rational, real
13. irrational, real
2. No, because it cannot be written as a
decimal that terminates or repeats.
14. whole numbers, integers, rational, real
Practice and Problem Solving: C
3. Yes, as long as the decimal is infinite
and nonrepeating, such as
0.31311311131111¡.
1. real, irrational
2. integers, rational, real
4. Yes, for example, 2 = 0.6 .
3
3. irrational, real
4. whole numbers, integers, rational, real
5. A decimal that is an irrational number is
infinite and nonrepeating, such as the
value for ¦Ð.
5. real, rational
6. real, rational, integer, whole
7. integers; possible points are positive
and negative numbers
6. Both are real numbers and both can be
written as decimals.
8. real; elevation can be any number
above or below zero
9. no; there are an infinite number of
rational numbers between any two
integers
Original content Copyright ? by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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