To estimate $0.87 \times 512$ by rounding, follow these steps:

1. Round 0.87: This can be rounded to 0.9 (since 0.87 is closer to 0.9 than 0.8).
2. Round 512: This can be rounded to 500 (since 512 is closer to 500 than 600).

Now, multiply the rounded numbers:

$0.9 \times 500 = 450$

So, the estimate of $0.87 \times 512$ by rounding is 450.

Would you like more details, or do you have any questions about this estimation?

Here are 5 related questions you might find helpful:

1. How would the estimation change if we used different rounding rules?
2. What is the exact value of $0.87 \times 512$?
3. How does rounding affect the accuracy of estimates in general?
4. What other methods could you use to estimate the product of two numbers?
5. How can we apply estimation in real-life scenarios?

Tip: When rounding, consider whether you need an overestimate or underestimate, as this can guide your rounding direction.