3. How many seconds are in 2.68 years?
ANSWER:8.45 x 107 s
SOLUTION:
Given: 2.68 years’
Desired: seconds (s)
We need to go from years to seconds. We can go from years to days, from days to hours, and from hours to seconds. Your roadmap will most likely look very different. My roadmap looks like this:
\(\displaystyle\mathbf{years\rightarrow{days}\rightarrow{hours}\rightarrow{seconds}}\)
My three equivalences are: 1 year = 365 days (we won’t worry about leap year), 1 day = 24 hours, 1 hour = 3600 s.
I can write 2 conversion factors for each equivalence:
\(\displaystyle\frac{1\;year}{365\;days}\;or\;\frac{365\;days}{1\;year}\)
\(\displaystyle\frac{1\;day}{24\;hours}\;or\;\frac{24\;hours}{1\;day}\)
\(\displaystyle\frac{1\;hour}{3600\;s}\;or\;\frac{3600\;s}{1\;hour}\)
Now I am ready to set up the problem starting with our given of 2.68 years.
\(\displaystyle\require{cancel}2.68\;\cancel{years}\times\frac{365\;\cancel{days}}{1\;\cancel{year}}\times\frac{24\;\cancel{hr}}{1\;\cancel{day}}\times\frac{3600\;s}{1\;\cancel{hr}}\;=\;\mathbf{8.45\times{10^7}\;s}\)
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