Rational vs Irrational
Categorize each example as rational or irrational
4.589
0.666...
1.732...
0.022022022022...
√5
√16
4.589 - rational (it can be expressed as a fraction: 4589/1000)
0.666... - rational (it can be expressed as a fraction: 2/3)
1.732... - irrational (non-repeating decimal with no pattern, approximates the square root of 3)
0.022022022022... - rational (it can be expressed as a fraction: 2/90)
√5 - irrational (non-repeating decimal with no pattern, approximates the square root of 5)
√16 - rational (it can be expressed as a whole number: 4)
Place each number into the categories it belongs.
(some numbers will go into more than one category)
Natural Whole Integers Rational Irrational Real
√81 √3 0 -13 1.2
Natural: 0, 1.2
Whole: 0
Integers: 0, -13
Rational: 0, 1.2
Irrational: √3
Real: √81, √3, 0, -13, 1.2
Express 1/6 as a repeating decimal.
To express 1/6 as a repeating decimal, we divide 1 by 6:
0.166666...
The number 6 does not terminate or repeat, so we can represent 1/6 as the repeating decimal 0.166666...
choose the point that represents √18 on the number line.
R S Q P
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___ because it is in between the perfect squares ___ and ___
To determine which point represents √18 on the number line, we need to find the perfect squares that √18 falls between.
Starting with perfect squares: 0, 1, 4, 9, 16, 25, ...
We can see that √18 falls between √16 (4) and √25 (5) on the number line.
Therefore, the point that represents √18 on the number line is between points Q and R:
R S Q P
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choose the point that represents √18 on the number line.
___ because it is in between the perfect squares ___ and ___.
R S Q P
|-|-|-|-|-|-|-|-|-|
To determine which point represents √18 on the number line, we need to find the perfect squares that √18 falls between.
Starting with perfect squares: 0, 1, 4, 9, 16, 25, ...
We can see that √18 falls between √16 (4) and √25 (5) on the number line.
Therefore, the point that represents √18 on the number line is between points Q and R:
R S Q P
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choose the point that represents √18 on the number line. (choose one)
___ because it is in between the perfect squares 16 and 25.
R S Q P
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