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I have a few questions here that is bothering me a little ..

  1. Is '$0$' an even and odd number ? Because $0$ divided by $2$ and $3$ will give you $0$ which is still a whole number

  2. Are numbers like $-3 , 7$ called a rational number ? Be fussier can be expressed as $\frac{-3}{1}$ or $\frac{7}{1}$ whereas numbers like $\pi$ cannot be expressed as $\frac{3.142}{1}$

  3. Is $120\%$ which is $\frac{6}{5}$ as a fraction an integer ?

  4. Is $120\%$ a rational number ?

smingerson
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user307640
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    For #1, note that the test for odd numbers isn't whether they are divisible by 3. (For example, 6 is divisible by 3 but is even.) Instead, odd numbers are the ones that are not even, i.e., they are not divisible by 2. – Théophile Feb 27 '16 at 15:22
  • The even/odd question is best considered in light of definitions. https://simple.wikipedia.org/wiki/Even_number https://simple.wikipedia.org/wiki/Odd_number – Tom Collinge Feb 27 '16 at 15:23

3 Answers3

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  1. $0$ is considered an even number. The number k is even if $k=2n$ for some integer (including $0$) and k is odd if $k=2n+1$ for some integer.

  2. A rational number is any number we can write as $\frac{a}{b}$, where $a,b$ are integers.

  3. $120\%$ is not an integer. The integers are ${..., -2, -1, 0, 1, 2, ...}$

  4. Since $120\%=\frac{6}{5}$, it is a rational number.

smingerson
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  1. $0$ is even, as is every second number in either positive or negative direction starting from $0$.
  2. Yes, they are all (expect for $\pi$) rational numbers. A rational number is one that can be written as a fraction with an integer both in the numerator and the denominator (this is what excludes $\pi$).
  3. $\frac{6}{5}$ is not an integer.
  4. $120\%=\frac{6}{5}$ is a rational number, as per the definition above.
Bobson Dugnutt
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I will answer questions as posed.

First yes 0 is an even number because there is an integer k such that 2k=0,that k is again 0 but that does not matter really.

Secondly,yes all integers are rational numbers and they can be expressed as you have written.Also very important is that there is no "pie" number,rather there is "Pi" also written as $\pi$.Numbers that can not be written as ratinals are called irrational numbers.Why they can not be written down is a property of real number system and usualy treated in introductory set theory books.

Thridly.The fractions are same thing as rational numbers.Rational numbers are called rational numbers because they represent a ratio between two numbers for example 3/2 and 5/6 .All integers are rationals,but not all rationals are integers.Only fractions which have 1 as denominator can be considered integers.

Percents are not numbers,but rather substitute for numbers.One percent means 0.01,in that sense yes 120% is 1.2 which can be written as 6/5 which is natural number.It is a hideous habit to think of percents as numbers,they are only a tool and nothing more.

TheCoolDrop
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