Identify the number that does not belong with the other three. Explain your reasoning. negative 10 over 2, negative 13.4, square root 18, 22.7 repeating 7

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Identify the number that does not belong with the other three. Explain your reasoning. negative 10 over 2, negative 13.4, square root 18, 22.7 repeating 7

Algebra
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|dw:1439785746788:dw| that doesn't belong because it's a repeating number
Explain the reason if you could please.
that doesn't belong because it's a repeating number

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or you can use number system
different types
\(\dfrac{10}{2}\) does not belong there because it is the only integer in the given list \(-13.4\) does not belong there because it is the only negative number \(\sqrt{18}\) does not belong there because it is the only irrational number
If I had to choose one, I would pick because \(\sqrt{18}\) as I feel irrational/rational is a more important difference compared to other
I have to agree with @ganeshie8 simplifying \[\sqrt{18} \] gives us \[\sqrt{18} \rightarrow \sqrt{9 \cdot 2} \rightarrow 3 \sqrt{2}\] \[\sqrt{2} \] is irrational because we can't express this as a fraction. as for the decimal choices, you can express that as a fraction (positive or negative...doesn't matter) for -13.4 -13.4 x 10 =-134 -134/10 = -13.4 similarly for 27.77 (yes the 7 is repeating, but for simplicity reasons I will just type 7 twice) 27.77 x 100 = 2777 2777/100 = 27.77 and \[-\frac{10}{2} \] can be reduced to \[-5\] that number as a fraction is \[\frac{-5}{1}\]
oops forgot to type that -5/1 is rational because it can be expressed as a fraction. You can view more examples here: http://www.mathsisfun.com/rational-numbers.html
$$x=2.777\dots\\10x=27.777\dots\\10x-x=25\\9x=25\\x=\frac{25}9$$ which is how you write a repeating decimal like that as a fraction
Identify the number that does not belong with the other three. Explain your reasoning. negative 10 over 2, negative 13.4, square root 18, 22.7 repeating 7 1) -10/2 = -5 (rational number) 2) -13.4 (terminating decimal) 3) square root 18 = 3 * square root 2 (irrational number) 4) 22.7 repeating 7 (non terminating repeating decimal) therfore,1) ,2) and 4) are rational numbers only 3) is irrational

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