Odd and even describe integer values. A decimal such as 3.4 is neither; a decimal such as 3.0 equals the odd integer 3.
Classify the value, not the punctuation
A non-integer decimal such as 4.7 is neither odd nor even. But saying that every number with a decimal point is excluded goes too far: 3.0 = 3, and 3 is an odd integer. Likewise, 8.000 = 8, which is even.
The relevant question is whether the value is an integer. Decimal notation is only one way of writing it. OpenStax’s introduction to number classifications distinguishes integers from the larger set of rational numbers, which also contains non-integer fractions and terminating decimals.
| Written value | Integer? | Parity |
|---|---|---|
| 3.0 | Yes, equals 3 | Odd |
| 8.000 | Yes, equals 8 | Even |
| −7.00 | Yes, equals −7 | Odd |
| 2.5 | No | Neither |
| 0.0 | Yes, equals 0 | Even |
Why the odd formula excludes 2.5
An odd integer has the form 2k + 1 for an integer k. If you try 2.5 = 2k + 1, the solution is k = 0.75. Since 0.75 is not an integer, the definition fails.
It is not enough to say that 2.5 cannot be divided into two equal integer groups. That description alone could accidentally classify every non-integer as odd. The starting requirement, that the number itself be an integer, is essential.
Fractions need the same care. 15/5 equals 3 and is odd. 15/4 equals 3.75 and has no integer parity. Simplify or evaluate the value before attaching the label.
Do not inspect the last displayed decimal digit
The final character of 3.0 is zero, but its value is odd. The last-digit shortcut applies to decimal integer notation, such as 3, without a fractional part.
Trailing zeros after a decimal point do not change value: 3.0 = 3.00. Appending a zero to the integer 3 produces 30, a different number. The location of that little dot is doing actual work.
What to enter in the calculator
The calculator accepts decimal integer notation without a decimal point. Enter 3 for 3.0, 8 for 8.000, and -7 for −7.00. A rejected spelling does not change the mathematical classification of its value.
Do not round a value such as 2.5 merely to obtain an odd/even result. Rounding creates a new value, and different rounding choices can produce different parity. For programming inputs, also consider large-integer precision: a stored approximation can differ from the number originally typed.