A piano tuner is trying to get the note A on a piano to have a frequency of exactly 440 hertz (H), or cycles per second. An electronic tuner capable of detecting a difference of x cycles per second costs 5/x dollars.
a. How much would it cost to make sure the note was within 1.0 H of 440?
b. How much would it cost to make sure the note was within 0.1 H of 440?
c. How much would it cost to make sure the note was within 0.01 H of 440?
Scientifically, two quantities are close if it requires an accurate measuring device to detect the difference. In real life, accuracy costs money. How much would it cost to measure the differences in the above circumstances?