3.2 Rational Numbers. Rational Number Any number that can be written in the form of a fraction. a...
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Transcript of 3.2 Rational Numbers. Rational Number Any number that can be written in the form of a fraction. a...
3.2
Rational Numbers
Rational Number
• Any number that can be written in the form of a fraction.
a
b
a and b have to be integers
0b
Write Each Number as a Rational Number
aka a Fraction
1.)66
a
37
6
.) 12b
12
1
Write Each Number as a Rational Number
aka a fraction
tens ones . tenths hundredths thousandths Ten - thousandths
.)0.84c84
100
21
25
.)5.875d875
51000758
How do you write a repeating decimal into a fraction?Writing Decimals as Fractions
Let me first introduce the shortcutIF and ONLY IF the bar notation is
COMPLETELY over ALL of the numbers after the decimal, you can use this shortcut.
9
88.0
99
1717.0
9999
50055005.0
DISCUSS: Do you notice a pattern?
Put all of the digits under bar notation in a fraction with the equal number of 9’s
Writing Decimals as FractionsNow for the rationale
17.0Let’s use algebra to find the fraction of
Let’s assign a variable 17.0n
Multiply both sides by 100 17.17100 nSubtract both sides by n nnn 17.17100
Substitute 17.017.17100 nn17.0n
Simplify 1799 n
Divide both sides by 99 99
17n
Examples
3.0
Write each decimal as a fraction in simplest form.
A)
54.0B)
213.0C)
9
3
3
1
99
54
11
6
999
213
333
71
Rational Vs. Irrational
Rational• Terminating or repeating
decimals
Irrational• Decimals that do not
terminate or repeat• Pi
Identify all Sets to which each number belongs
a.) 0Whole, Integer, Rationalb.) 1.313313331…Irrationalc.) 1.45Rationald.) -4Integer, Rational
4.)15
e rational
Homework
CA Math Page 104 (12-48) even