The earth’s age, 4.5 billion years old, is compared to 1 month consisting of 31 days. Mammals first appeared 210 million years ago. When did mammals firs appear in the course of a month? Round to the nearest day.

1. Convert the earth's age and the time of the first appearance of mammals into the same unit:
4.5 \text{ billion years} = 4.5 \times 10^9 \text{ years}
210 \text{ million years} = 210 \times 10^6 \text{ years}

2. Calculate the proportion of the time when mammals appeared:
\text{Proportion} = \frac{210 \times 10^6}{4.5 \times 10^9} = \frac{210}{4500} = 0.0467

3. Convert this proportion into days considering 1 month = 31 days:
\text{Days} = 31 \times 0.0467 = 1.44

4. Round the result to the nearest day:
\text{Days} \approx 1 \text{ day}

So, mammals first appeared on approximately the 1st day of the month.