convert 0.510 in/ms to km/hr?

Question

basically I set it up like this: 0.510 in/1 ms x 2.54 cm/1 in x 1 km/10000 cm x 10 to -3 power ms/ 1 s x 60s/1 hr. They are getting 46.6 km/hr and I am getting some ridiculously small number?

Answer 1

You have three problems in you equation:

1)
1km= 1 00 000 cm NOT 1 0 000 (so you answer was off by a factor of 10 to start with)

2) There are 60 minutes in a hour not 60 seconds so there are 60^2 or 3600 seconds in an hour (so you answer was off by a factor of 60 multipled by the original 10)


3) There are 10^3 ms per second sec NOT 10^-3
(so you answer was off by a factor of 10^6 times the 600 that you had from the first two mistakes)

SO your answer is 1/6*10^8 of what the answer should be---
Multiple you answer by 6 00 000 000 (600 million) and see if it is around 45 (what I got doing the math in my head)

Answer 2

You can avoid such complications by splitting the problem into small steps.

1) First we convert 0.510 in/ms to per hour, by mutliplying with first with 1000 (1 second has 1000 milliseconds) and then multiplying by 3600 (1 hour has 60 minutes and each minute is 60 seconds, so 1 hour has 60 X 60 = 3600 seconds). So, the value becomes 1836000

2) Now we convert inches to cms. by multiplying with 2.54, and get 1836000 X 2.54 = 4663440 cms / hr.

3) Now we convert this to kilometers per hour by dividing with 100,000 (1 meter has 100 centimeters and 1 kilometer has 1000 meters). So, we get 46.6344 km/hr.

I hope you got the logic?

Answer 3

I see three errors:

1 km/10000 cm should be 100,000.

10 to -3 power ms/ 1 s should be 1,000 ms / 1 s.

60s/1 hr should be 3,600.