To convert 0.60 milliliters into a fraction, we can express it as \( \frac{60}{100} \) since 0.60 is equivalent to 60 out of 100.
Next, we simplify \( \frac{60}{100} \). We do this by dividing both the numerator and the denominator by their greatest common divisor, which is 20:
\[ \frac{60 \div 20}{100 \div 20} = \frac{3}{5} \]
Thus, the fraction that shows how many milliliters of the liquid Randall needs to pour into the beaker is \( \frac{3}{5} \).