Question

Finley thinks of a number, r. He rounds r to 3 significant figures. He then rounds the result to 2 significant figures. His final result is 470. What is the smallest value that r could have?

Answer 1

The smallest value that r could have is 465.

To find the smallest value that r could have, we need to reverse the rounding process. First, we know that the final rounded value is 470, which has two significant figures. So, r rounded to 3 significant figures must have a value between 465 and 475. Next, we reverse the rounding to 2 significant figures.

Since the final result is 470, r rounded to 2 significant figures could be 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, or 475. Therefore, the smallest value that r could have is 465.