Convert angles from the sexagecimal system to centesimal one 
How do you convert angles from the sexagecimal system to centesimal one?

For example 
63 degrees 14 minutes 51 seconds reduced to centesimal ??
Here's how it's done but I don't understand the steps:  image at postimg

I write the conversion factors so that it looks clearer:
$$51'' = 51'' \cdot \frac{1'}{60''} = \left(\frac{51}{60}\right)' = \left(\frac{17}{20}\right)' = 0.85'$$
So,
$$14'51'' = 14.85' = 14.85' \cdot \frac{1^\circ}{60'} = 0.2475^\circ$$
and thus,
$$63^\circ 14'51'' = 63.2475^\circ = 63.2475^\circ \cdot \frac{1 \text{ rt. angle}}{90^\circ} = 0.70275 \text{ rt. angle} $$
$$= 0.70275 \text{ rt. angle} \cdot \frac{100^g}{1 \text{ rt. angle}}= 70.275^g$$
