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15 Cards in this Set

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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.
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.
Irrational

Example: 5/0 = undefined
The ___________ form of a rational number either terminates or is periodic.
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).
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... _____________
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. ___________
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.
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 C
group B
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? _____
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