2.1 and 2.2: rational numbers. main idea/vocabulary rational number terminating decimal repeating...
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2.1 and 2.2: RATIONAL NUMBERS
• rational number
• terminating decimal
• repeating decimal
• bar notation
• Express rational numbers as decimals and decimals as fractions.
Write a Fraction as a Decimal
Write as a decimal.
0
–160
.1
–128
8
0–112
75
14
12
80–80
0
Divide 3 by 16.
Answer: 0.1875
1. A
2. B
3. C
4. D0% 0%0%0%
A. 0.0515
B. 0.0625
C. 0.0875
D. 0.16
Write a Repeating Decimal
You can divide as shown in Example 1 or use a calculator.
Answer:
–35 11 –3.18181818ENTER÷
1. A
2. B
3. C
4. D0% 0%0%0%
A. 5.1
B. 5.15
C. 5.2
D. 5.9
AGRICULTURE A farmer lost the fruit on 8 of 15 orange trees because of unexpected freezing temperatures. Find the fraction of the orange trees that did not produce fruit. Express your answer as a decimal rounded to the nearest thousandth.
To find the fraction of trees that did not produce fruit, divide the number of lost trees, 8, by the total number of trees, 15.
Round a Repeating Decimal
8 15 0.5333333333ENTER÷
Look at the digit to the right of the thousandths place. Round down since 3 < 5.
Answer: The fraction of fruit trees that did not produce fruit was 0.533.
Round a Repeating Decimal
1. A
2. B
3. C
4. D0% 0%0%0%
A. 0.094
B. 0.148
C. 0.182
D. 0.252
SCHOOL In Mrs. Townley’s eighth grade science class, 4 out of 22 students did not turn in their homework. Find the fraction of the students who did not turn in their homework. Express your answer as a decimal rounded to the nearest thousandth.
Write 0.32 as a fraction.
0.32 is 32 hundredths.
Write a Decimal as a Fraction
Simplify.
Answer:
1. A
2. B
3. C
4. D0% 0%0%0%
Write 0.16 as a fraction.
A.
B.
C.
D.
Write a Decimal as a Fraction
ALGEBRA Write 2.7 as a mixed number.
Multiply N by 10 because 1 digit repeats.
Let N = 2.7 or 2.777... . Then 10N = 27.777... .
Subtract N = 2.777... to eliminate the repeating part, 0.777... .
Divide each side by 9.
Write a Decimal as a Fraction
Answer:
9N = 25 10N – 1N = 9N
10N = 27.777...–1N = 2.777...
Simplify.
1. A
2. B
3. C
4. D0% 0%0%0%
ALGEBRA Write 1.7 as a mixed number.
A.
B.
C.
D.
End of the Lesson
Compare Positive Rational Numbers
Write as fractions with the same denominator.
Replace ■ with <, >, or = to make ■ a true sentence.
Answer:
1. A
2. B
3. C
A B C
0% 0%0%
A. >
B. <
C. =
Replace ■ with <, >, or = to make ■ a true sentence.
Compare Using Decimals
Express as a decimal.
Answer:
Replace ■ with <, >, or = to make 0.7 ■ a true sentence.
■
■
In the tenths place, 7 > 6.
1. A
2. B
3. C
A B C
0% 0%0%
A. >
B. <
C. =
Replace ■ with <, >, or = to make ■ 0.5 a true sentence.
CHEMISTRY The values for the approximate densities of various substances are shown in the table. Order the densities from least to greatest.
Order Rational Numbers
Write each fraction as a decimal.
Order Rational Numbers
Answer: From the least to the greatest, the densities are
So, the nylon is the least dense, and aluminum is the most dense.
1. A
2. B
3. C
4. D
0% 0%0%0%
AMUSEMENT PARKS The ride times for five amusement park attractions are shown in the table. Order the lengths from least to greatest.
A.
B.
C.
D.
Replace ■ with <, >, or = to make –4.62 ■ –4.7 a true sentence.
Graph the decimals on a number line.
Answer: Since –4.62 is to the right of –4.7, –4.62 > –4.7.
Compare Negative Rational Numbers
1. A
2. B
3. C
A B C
0% 0%0%
A. <
B. >
C. =
Replace ■ with <, >, or = to make –2.67 ■ –2.7 a true sentence.
Since the denominators are the same, compare the numerators.
Compare Negative Rational Numbers
Replace ■ with <, >, or = to make a true sentence.
Answer:
1. A
2. B
3. C
A B C
0% 0%0%
A. >
B. <
C. =
Replace ■ with <, >, or = to make a true sentence.
End of the Lesson