rational and irrational numbers. classifying numbers numbers can be classified for instance, we can...
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![Page 1: Rational and Irrational Numbers. Classifying Numbers Numbers can be classified For instance, we can pick out all of the numbers that are divisible by](https://reader035.vdocuments.site/reader035/viewer/2022072008/56649d845503460f94a6b661/html5/thumbnails/1.jpg)
Rational and Irrational Numbers
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Classifying Numbers
• Numbers can be classified
• For instance, we can pick out all of the numbers that are divisible by 2. They are classified as even numbers.
• We can also classify numbers in other ways.
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Rational and Irrational
• Numbers can be classified as rational numbers.
• Rational numbers are numbers that in decimal form, are either terminating OR repeating.
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Terminating numbers
• A terminating number is a number that terminates, which means ends.
• Examples of terminating numbers:
3.14 4.5678932221 0.33339
• Examples of numbers that do NOT terminate (do not end)
3.333333… pi 0.121231234….
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Repeating Numbers
• A repeating number is a number that does not terminate, but it repeats over and over EXACTLY THE SAME WAY
• Examples of repeating numbers:
3.33333…. 4.34343434……
Examples of NON-repeating numbers:
3.343453456….. pi 9.352109….
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Rational vs. Irrational
• If a number repeats exactly, or terminates, then it is a rational number.
• If a real number is NOT rational, then it is irrational.
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Rational or irrational?
7
3
2
6.2533678
1 rational irrational
irrational rational
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Real Numbers
• Another classification of numbers is the set of numbers called Real Numbers.
• This one is easy. Real numbers are the rational numbers and the irrational numbers combined.
• Real = Rational + Irrational
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• Place the following numbers in order from least to greatest.
-7, 14/3, 280%, 1 3/7
Step 1. Change into decimals.
Step 2. Place on a number line.
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-7 = -7.0
14/3 = 14 divided by 3 4.7
280% = 280 divided by 100 2.8
1 3/7 = 1 + 3/7 1.43
0
-7 280% 14/31 3/7
Order from least to greatest: -7, 1 3/7, 280%, 14/3
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Do Example 1 NowExample 1
Order numbers from least to greatest; place on number line: 5/6 4 ¼ 300% 0. 23 3/10
Step 1: Convert to decimals:
5/6 = ______ 4 ¼ = ______
300% = ______
0. 23 = ______ 3/10 = ______
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Example 1
Step 1: Convert to decimals:
5/6 = 0.833 4 ¼ = 4.25 300% = 3.0
0. 23 = 0.23 3/10 = 0.3
Order from least to greatest:
0.23, 0.3, 0.833, 3.0, 4.25
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0.23, 0.3, 0.833, 3.0, 4.25
0
0.23 0.833 3.0
0.3
4.25
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Example 2
• Which is smaller: -2 or -3
• -3 is smaller
• Convert -3 ½ to decimal form
• -3 + - ½ = -3 + -0.5 = -3.5