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Variation
Variation
Variation(not
exhaustive)
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Objective: You will be able to compare an irrational number to a rational number or to
another irrational number.
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Comparing Irrational and Rational Numbers
8.213 ____ 8.23
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Comparing Irrational and Rational Numbers
8.213 ____ 8.23
8.2138.23
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Comparing Irrational and Rational Numbers
- 8 ____ -7
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Comparing Irrational and Rational Numbers
- 8 ____ -7
-8 -7
0 1-1
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Comparing Irrational and Rational Numbers
- 8 ____ -7
-8 -7 0 1-1
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Comparing Irrational and Rational Numbers
Fractions as decimals
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Comparing Irrational and Rational Numbers
Fractions as decimals
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Comparing Irrational and Rational Numbers
Fractions as decimals
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Comparing Irrational and Rational Numbers
Fractions as decimals
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Comparing Irrational and Rational Numbers
Fractions as decimals
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Comparing Irrational and Rational Numbers
Fractions as decimals
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Comparing Irrational and Rational Numbers
Fractions as decimals
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Comparing Irrational and Rational Numbers
Fractions as decimals
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Comparing Irrational and Rational Numbers
Comparing Irrationals is the Same Process!
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Comparing Irrational and Rational Numbers
The …
1.124… ____ 1.2
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Comparing Irrational and Rational Numbers
The …
1.124… ____ 1.2
1.124…1.2
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Comparing Irrational and Rational Numbers
Pi or ∏
____ 3.14∏
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Comparing Irrational and Rational Numbers
Pi ∏
____ 3.14∏
3.143.14159…
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Comparing Irrational and Rational Numbers
Pi ∏
____ 3.14∏
3.143.14159…
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Comparing Irrational and Rational Numbers
Radicals
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Comparing Irrational and Rational Numbers
Radicals
32
√ 4 √ 9
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Comparing Irrational and Rational Numbers
Radicals
32 2.5
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Comparing Irrational and Rational Numbers
Radicals
32
√ 4 √ 9√ 7
2.5
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Comparing Irrational and Rational Numbers
Radicals
____ 4.5
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Comparing Irrational and Rational Numbers
Radicals
____ 4.5
54 4.5
√ 16 25
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Comparing Irrational and Rational Numbers
Radicals
____ 4.5
54 4.5
√ 16 25√ 18
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Comparing Irrational and Rational Numbers
Practice
For each problem, decide which of the two numbers is greater and place a > or < sign to
indicate the greater number:
1.341 _____ 1.341...
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Comparing Irrational and Rational Numbers
Practice
For each problem, decide which of the two numbers is greater and place a > or < sign to
indicate the greater number:
1.341 _____ 1.341...
1.3411.341 . . .
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Comparing Irrational and Rational Numbers
Practice
For each problem, decide which of the two numbers is greater and place a > or < sign to
indicate the greater number:
1/3 ______ 0.3132...
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Comparing Irrational and Rational Numbers
Practice
For each problem, decide which of the two numbers is greater and place a > or < sign to
indicate the greater number:
1/3 ______ 0.3132...
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Comparing Irrational and Rational Numbers
Practice
For each problem, decide which of the two numbers is greater and place a > or < sign to
indicate the greater number:
1/3 ______ 0.3132...
0.3330.3132
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Comparing Irrational and Rational Numbers
Practice
For each problem, decide which of the two numbers is greater and place a > or < sign to
indicate the greater number:
- ______ -3.2
∏
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Comparing Irrational and Rational Numbers
Practice
For each problem, decide which of the two numbers is greater and place a > or < sign to
indicate the greater number:
- ______ -3.2
∏-3.14159-3.2
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Comparing Irrational and Rational Numbers
Practice
For each problem, decide which of the two numbers is greater and place a > or < sign to
indicate the greater number:
______ 9.7
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Comparing Irrational and Rational Numbers
Practice
For each problem, decide which of the two numbers is greater and place a > or < sign to
indicate the greater number:
______ 9.7
109
√ 81 √ 100
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Comparing Irrational and Rational Numbers
Practice
For each problem, decide which of the two numbers is greater and place a > or < sign to
indicate the greater number:
______ 9.7
109 9.5
√ 81 √ 100√ 85
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Comparing Irrational and Rational Numbers
Practice
For each problem, decide which of the two numbers is greater and place a > or < sign to
indicate the greater number:
______ 9.7
109 9.5
√ 81 √ 100√ 85
9.7
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Conclusion: You can now compare an irrational number to a rational number or to
another irrational number.