To solve the problem of finding the upper and lower bounds for the number $p$, when rounded to 2 decimal places and equal to 0.02:

1. Understand the range of rounding:

   • When a number $p$ is rounded to 2 decimal places, it is rounded to the nearest hundredth. The lower and upper bounds are determined by considering the interval within which any number rounds to $0.02$.
   • The lower bound is the smallest number that rounds up to $0.02$, and the upper bound is the largest number that still rounds down to $0.02$.

2. Lower bound calculation:

   • The smallest number that rounds to $0.02$ is $0.015$. This is because $0.015$ rounds up to $0.02$, but anything smaller (like $0.0149$) rounds to $0.01$.

3. Upper bound calculation:

   • The largest number that rounds to $0.02$ is $0.024999\ldots$ (effectively $0.025$ when truncated), since $0.025$ would round up to $0.03$.

Final Answer:

• Lower bound: $0.015$
• Upper bound: $0.025$

Let me know if you'd like further explanation or help! Here are some questions for deeper understanding:

1. Why is the lower bound $0.015$ instead of $0.02$?
2. How does rounding affect the precision of numbers in real-world scenarios?
3. Can you think of another example where upper and lower bounds would be useful?
4. What changes if we round $p$ to 1 decimal place instead?
5. How would these bounds change if the rounding rule was "round down only"?

Tip: Always think of bounds as capturing the "range of validity" for rounding.