College Mathematics Real Numbers 2
Terms
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- A __________ number is a number that can be written in the form of a/b, where a and b are integers, and b does not equal 0.
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Rational.
Examples: -3
5/4 = 1.25
1/3 = 0.33
Whole numbers can be written with a denominator of 1, so they count as rational numbers (i.e. -3 = -3/1, 15 = 15/1) - An ____________ number cannot be written in the form of a/b, where a and b are integers, and b does not equal 0.
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Irrational
Example: 5/0 = undefined - The ___________ form of a rational number either terminates or is periodic.
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Decimal.
3/4 = 0.75 this decimal terminates
1/6 = 0.16666... this is a periodic decimal as it has a repeating pattern: also written 0.16
6/33 = 0.181818... this is also a periodic decimal as it has a repeating pattern: also written 0.18 - In decimal form, ____________ numbers neither terminate nor are periodic (no repeating pattern).
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Irrational
Example: 3/65 = 0.04651538...
Ö3 = 1.7320508... (the square root of 3 is an infinite decimal) - Is the following number rational or irrational? 4.123696857... _____________
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Irrational
4.123696857... is neither periodic, nor does it terminate. It appears to continue with no apparent pattern. - Is the following number rational or irrational? 2.135135. ___________
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Rational
2.315315 has a clear cut repetitive pattern and ends after the second 5. -
Which of the following is a rational number?
3.245245⬦
all of the other choices
3.24...
3.245 -
All of the other choices.
3.245245... is periodic, 3.245 terminates, and 3.24... is periodic. -
Which of the following is an irrational number?
Ö2
1.45
-5
1/10 - √2 = 1.4142135... It doesn’t terminate, nor is it periodic.
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Which of the following is a rational number?
3.14159⬦
1.2564513...
2.54586⬦
1.33333⬦ -
1.33333...
None of the numbers terminate, but 1.33333... is periodic. -
In group A, there are 5 cupcakes for 3 children. In group B, there are 7 cupcakes for 4 children, and in group C, there are 9 cupcakes for 5 children. Which group (if any) represents an irrational number of cupcakes per child?
group A< -
None of the other choices.
Group A = 5/3 cupcakes per child. Group B = 7/4 cupcakes per child. Group C = 9/5 cupcakes per child, all of which are rational numbers. -
Which of the following is a rational number?
√18
√20
√25
√22 -
√25.
√18 = 4.2426...
√20 = 4.4721...
√22 = 4.6904
√25 = 5 -
Which of the following is an irrational number?
-Pi (P)
2.4646
(1/5)2
-1 -
-Pi. Pi is a value used in calculating the circumference and area of circles, and is a nonterminating, nonperiodic decimal:
P = 3.141592654...
When using Pi in calculations, generally you just use a rounded off value of 3.14. - Which of the following (A, B, C or D) on the number line BEST represents an irrational number? _____
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C
A, B and D clearly land on either whole numbers or perfect fractions. -
Which of the following is a rational number?
(√7)2
√18
√20
(√5) -
(√7)2
If you square the square root of a number, it gets rid of the radical (Ö). So (√7)2 = 7 -
Which of the following is an irrational number?
Pi / Pi
√2 / √2
(√15) / 2
(√4) / 2 -
(√15) / 2
(√15) / 2 = 1.9365...
(√4) / 2 = 2 / 2 = 1
√2 / √2 = 1
Pi / Pi = 1