# Decimal - can they be even or odd?

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

1. ### School Boy ErrorOccasional 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. ### bombaysapphireStar 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 ErrorOccasional commenter

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

4. ### AnonymousNew 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 ErrorOccasional commenter

Thanks, it did certainly prompt a healthy discussion!

6. ### Vicky496

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. ### Vicky496

If you type 'number sets' into google images there's some diagrams that might be clearer than my waffle!

8. ### School Boy ErrorOccasional commenter

Thanks, I'll have a peek.