Algebra 1

Name The Subsets Of The Real Numbers To Which Each Number Belongs:
A.-2.324
B.Square Root Of 46

I don't even know what this stuff means. Please help!

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  1. A) Real/Rational
    B) Real/Irrational

    because -2.324 = (-2324/1000)
    but sqrt(46) cannot be expressed as a fraction

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  2. There are various classes of numbers. In order of increasing "size" we have

    whole numbers: 1,2,3,4,...
    integers: ...-3,-2,-1,0,1,2,3,...
    rational numbers (fractions): 1/2, 3/7, 98/113, etc
    Rational numbers include also
    terminating decimals: 2.5, 123.456, 99.32764, etc.
    repeating decimals: 1.22222..., 9831279.2397239239239...

    irrational numbers: everything else. They are decimal numbers which go on forever without repeating. Such as

    √7 = 2.64575...
    π = 3.14159265...
    and so on

    roots may be rational or even integers, if the radicand is a perfect power:

    √36 = 6 because 6^2 = 36
    √2.25 = 1.5 because 1.5^2 = 2.25
    ∛27 = 3 because 3^3 = 27
    and so forth

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