Step 1: Know what integers can hold.
Integer storage handles whole numbers like $5$, $100$, or $-20$. It has no place for a fractional part.
Step 2: Notice many values have fractions.
Science and engineering use numbers like $3.14$, $0.005$, and $125.78$ that carry a decimal point.
Step 3: Recall the floating-point form.
Floating-point stores a number as $\text{Mantissa} \times \text{Base}^{\text{Exponent}}$.
Step 4: See why this form helps.
By shifting the exponent, this form can show both very large and very small numbers, including fractions.
Step 5: Match the use to the options.
Characters use text codes, integers are whole numbers, and logic values are just true or false. None of these need fractions.
Step 6: Pick the right one.
Floating-point is built for real numbers, which is option (C).
\[ \boxed{\text{Real numbers}} \]