math- please help

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What is the best sequence of names to identify this set of numbers?
(1 3/5,-10, 0.51(the one is repeating), TT,17)
1.(rational,integer,irrational,irrational,natural)
2. (rational,irrational,rational, irrational, whole)
3.rational,real,rational,real, natural)
4. (real,integer, irrational,irrational,natural)

Off the bat I got rid of choices 2 and 3.
I picked choice#1 since a rational number is more specific and a real number can be rational or irrational.
Is this correct?
If I am not correct is there a website to hook me up with to explain the responses
Thank you

  • math- please help -

    0.51111... is rational, as are all numbers with repeating decimal places. Its value is 0.5 + 1/90 = 23/45

    so, the most specific ordering is

    rational,integer,rational,irrational,natural

    Looks to me like #3 is closest, since rational and irrational are mutually exclusive, and #1,2,4 all have "irrational" in a spot where the value is rational.

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