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Decimal - can they be even or odd?

Discussion in 'Mathematics' started by School Boy Error, Apr 22, 2012.

  1. School Boy Error

    School Boy Error Occasional commenter

    I know the answer to this is no as an even or odd number refer to a whole number but, my question is, is there a name for a decimal number then? My Year 5 class and I were debating this the other day, if a decimal number can't be odd or even what is it?
  2. bombaysapphire

    bombaysapphire Star commenter

    Only whole numbers can be odd or even. It wouldn't make sense to define a decimal as odd based on its ending if 3.5 is odd, what about 3.50?
    It's not an integer so it's neither.
  3. School Boy Error

    School Boy Error Occasional commenter

    Thanks, that's what we concluded in the end but it seemed a little obscure that it was almost left as "undefined"
  4. Anonymous

    Anonymous New commenter

    What is the definition of an odd number? A standard response is one "which ends in 1,3,5, 7 or 9". You might be lucky and get someone saying the units are "1,3,5,7 or 9". Explore further and you define an even number as one that can be put into 2 equal groups and an odd number can't because you get an odd one out.
    Someone might then point out that 3 is even because if you half it, you get 1 1/2 in both groups and since 1 1/2 is the same amount in both groups, you have even amounts in both groups.
    So you need to add to the definition that an even number is a whole number that can be split into 2 to make groups with the same amount in (again - whole numbers) with nothing left over.
    It's an interesting one to explore - can they truly define an odd and even number? Once they have explored that, the decimal makes sense.
  5. School Boy Error

    School Boy Error Occasional commenter

    Thanks, it did certainly prompt a healthy discussion!
  6. All numbers students come across up to the end of A-level are in the set of Real numbers. Any decimal that recurs or stops is also in the set of Rational numbers and can be written as a fraction (ie not Pi).

    So you could say integers (or natural numbers) can be even or odd; Real numbers can be rational or irrational - that might be difficult for year 5? (I teach A-level and am a bit out of touch with when students encounter Pi - which is the first number they will meet that can't be written as a fraction).
  7. If you type 'number sets' into google images there's some diagrams that might be clearer than my waffle!
  8. School Boy Error

    School Boy Error Occasional commenter

    Thanks, I'll have a peek.

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