Tutorial 1.6: Part 1

Dimensional analysis: time conversions

How do we calculate the number of minutes in 4.25 years?

If you need to get your bearings, start with the unit given, years, and write out conversion factors (as units) until you arrive at the desired unit - the minute.

\[ years \times \frac{days}{ year} \times \frac{hour}{day} \times \frac{minutes}{hour} \]

Complete with numerical conversion factors.

\begin{align*} & 4.25\, years \times \frac{365.25\, days}{ year} \times \frac{24\, hour}{day} \times \frac{60 \, minutes}{hour} \\ & = 2235330\, minutes \\ & = 2.24 \times 10^6 \, minutes \end{align*}

How do we calculate the number of years equivalent to 4.25 seconds?

If you need to get your bearings, start with the unit given, seconds, and write out conversion factors (as units) until you arrive at the desired unit - the year.

\[ second \times \frac{minute}{second} \times \frac{hour}{minute} \times \frac{day}{hour} \times \frac{year}{day} \]

Complete with numerical conversion factors.

\begin{align*} & 4.25\, s \times \frac{1 \,min}{60 \,s} \times \frac{1 \,hour}{60 \,min} \times \frac{1 \,day}{24 \,hour} \times \frac{1 \,year}{365.25 \,day}\\ & = 1.3467 \times 10^{-7}\, years \\ & =1.35\times 10^{-7}\, years \end{align*}

How do we calculate the number of milliseconds in a day?

If you need to get your bearings, start with the unit given, seconds, and write out conversion factors (as units) until you arrive at the desired unit - the year.

\[ day \times \frac{hour}{day} \times \frac{minute}{hour} \times \frac{seconds}{minute} \times \frac{milliseconds}{seconds} \]

Complete with numerical conversion factors.

\begin{align*} & 1.00 days \times \frac{24 \,hour}{day} \times \frac{60\,min}{hour} \times \frac{60\,s}{min} \times \frac{10^3\, ms}{s}\\ & = 86400000 \,ms \\ & =8.64\times 10^{7}\, ms \end{align*}