Fairly simple dimensional analysis- somehow gone wrong

[tigerlili]

Homework Statement

For about 10 years after the French Revolution, the French government attempted to base measures of time on multiples of ten: One week consisted of 10 days, one day consisted of 10 hours, one hour consisted of 100 minutes, and one minute consisted of 100 seconds. What are the ratios of (a) the French decimal week to the standard week and (b) the French decimal second to the standard second? Assume that the definition of a "day" remains the same.

Homework Equations

i know that for part A, you can do a simple ratio of 10/7 to get the correct answer of 1.43

for part B, I converted 1 french week into 1,000,000 french seconds
and 1 standard week into 86,400 seconds, originally, but i thought i had messed up.. so i got 604,800 the second time. i know that the first value i got is correct, because the correct answer is .864. I'm just having trouble recalling how i got that number, because i erased my work.. and, furthermore, i thought that the ratio was of french to standard, not vice versa. either way, 86400/1000000 is not .864, it is .0864. so obviously some number must be wrong, whether it is 1,000,000 or 86,400, but i have done the calculation over many times, and cannot find my mistake..as silly as that sounds :X

The Attempt at a Solution

woops.. see above!

 

[tms]

[ i thought that the ratio was of french to standard, not vice versa.

That's what you wrote in the statement of the problem.


To get the correct answer, you must compare the number of normal seconds and revolutionary seconds in the same period, for example a day. You have compared the number in a normal week and a revolutionary week, which are different periods.

 

[tigerlili]

okay, so i found my mistakes.. but, still, the question says to do a ratio of french to standard.. but 100,000/86,400 is not .864 which is the textbook's correct answer. it would have to be 86,400/100,000.. which is not what the question asks for, which is why i am confused

thanks for your help

 

[Redbelly98]

1 French second = 1/100,000 day.

So:

French second / standard second

= ( ? days) / ( ? days)​

Note the "days" units cancel, leaving a numerical ratio.

 

[tigerlili]

ahh i get it now, thanks so much!