You are going on a field trip in a school bus. A special detector placed on one of the bus's tires counts the number of rotation
s completed by the tire during the journey. The tire's diameter is 1 meter, and it made 8000 rotations during the trip. How far did the bus travel? Give an exact answer.
The way tires on wheels work is that when the wheel turns one complete turn, it moves (forward or backward) by a distance that's the circumference of the tire.
Now, we know that the circumference of a circle is (π) times the diameter. The diameter of the tire on this bus is 1 meter. So its circumference is (π · 1 meter), and every time it turns once, the bus moves 1 meter down the road.
If the tire rotated 8,000 times, then the bus moved 8,000π meters, or 8π kilometers.
THAT's the exact answer. If you want to know how far that actually is, then you take some number that's approximately π and multiply it by 8 km. You can never get an exact answer like that, because you can never write the exact value of π with digits.
In school, we often use ' 3.14 ' for π . If you do that, then the bus traveled
(8 km) x (3.14) = 25.1 kilometers .
When you do that, you have to remember that it's approximate. If you want an exact answer, then you have to leave π in the answer.
