Complex measurement and simple measurement

The one that includes more than one type of unit is known as complex measurement.

$$2^\circ \ 23' \ 12''$$

$$2h \ 23\mbox{min} \ 12\mbox{s}$$

The simple measurement is the one that uses only one type of unit.

$2,25$ hours

$135$ minutes

If, for example, we want to convert $2\mbox{h} \ 23\mbox{min} \ 12\mbox{s}$ into seconds, it is necessary to use the conversion factors to find all three values in seconds, and finally add them up.

$$2\mbox{h} \cdot \dfrac{60\mbox{min}}{1\mbox{h}}\cdot\dfrac{60\mbox{s}}{1\mbox{min}}=7.200\mbox{s}$$

$$23\mbox{min}\cdot\dfrac{60\mbox{s}}{1\mbox{min}}=1.380\mbox{s}$$

$$12\mbox{s}$$

$$7.200+1.380+12=8.592\mbox{s}$$

Converting from simple measurement to complex measurement

Two cases will be analyzed:

1.- Converting from minor units in to higher units: $7.523$ seconds into seconds, minutes and hours.

In this case, it will be necessary to divide by $60$ twice.

$$\begin{eqnarray} &7523'' & |\underline{60} & & \\\\ & 23'' & 125' & |\underline{60} \\\\ & & 5' & 2^\circ \end{eqnarray}$$

$$7523''=2^\circ \ 5' \ 23''$$

2.- Converting to lower units: $3,38$ hours to seconds, minutes and hours.

In this case it will be necessary to multiply by $60$.

$$3,38\mbox{h} \left\{ \begin{array}{c} 3\mbox{h} \\ 0,38\cdot60=22,8\mbox{min} \end{array} \right. \rightarrow 22,8\mbox{min}$$

$$22,8\mbox{min} \left\{ \begin{array}{c} 22\mbox{min} \\ 0,8\cdot60=48\mbox{s} \end{array} \right.$$

Namely,

$3,38\mbox{h} = 3h \ 22' \ 48''$