Question

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

Answer 1

that doesn't belong because it's a repeating number

Answer 2

Explain the reason if you could please.

Answer 3

that doesn't belong because it's a repeating number

Answer 4

or you can use number system

Answer 5

different types

Answer 6

\(\dfrac{10}{2}\) 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

Answer 7

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

Answer 8

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
\[\frac{-5}{1}\]

Answer 9

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

Answer 10

$$x=2.777\dots\\10x=27.777\dots\\10x-x=25\\9x=25\\x=\frac{25}9$$ which is how you write a repeating decimal like that as a fraction

Answer 11

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