What is part / whole?

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For example,

$$\frac{\text{part}}{\text{whole}} \cdot 100 = \text{percentage}$$

Example

$$\frac{1}{4} \cdot 100 \%$$

What is the quantity $\frac{\text{part}}{\text{whole}}$ called?

From the above example, it would yield $0.25$; what is the mathematical term for this quantity?

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Your specific example seems to be a rational number (fraction) between $0$ and $1$.

So the term Portion (a private case of Fraction) would probably be the most appropriate.