How can I convert degrees to grades using a conversion factor?

[Drain Brain]

please explain to me how can I utilize this conversion factor to convert degrees to grades

the book says,

$90^{\circ}=100^g$

$\therefore$ $1^{\circ}=\frac{10^g}{9}$ and $1^g=\frac{9^{\circ}}{10}$ - I don't know how to use this in actual convertion please help.

 

[Evgeny.Makarov]

I don't know how to use this in actual convertion

Suppose you want to convert an angle measure from degrees to grades.

Step 1: Represent the number of degrees as a product by 1. For example, rewrite $45^\circ$ as $45\cdot1^\circ$.

Step 2: Replace $1^\circ$ by the quantity from your post, i.e., $\left(\frac{10}{9}\right)^g$. In this example,you get $45\cdot\left(\frac{10}{9}\right)^g=50^g$.

Similarly, to convert from grades to degrees, represent $x^g$ as $x\cdot1^g$ and then replace $1^g$ by $\left(\frac{9}{10}\right)^\circ$. For example,
\[
30^g=30\cdot1^g= 30\cdot\left(\frac{9}{10}\right)^\circ =27^\circ.
\]