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

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To convert degrees to grades, use the conversion factor where $90^{\circ} = 100^g$, leading to $1^{\circ} = \frac{10^g}{9}$ and $1^g = \frac{9^{\circ}}{10}$. Start by rewriting the angle in degrees as a product, such as $45^\circ = 45 \cdot 1^\circ$. Replace $1^\circ$ with $\left(\frac{10}{9}\right)^g$, resulting in $45 \cdot \left(\frac{10}{9}\right)^g = 50^g$. For converting grades to degrees, represent $x^g$ as $x \cdot 1^g$ and substitute $1^g$ with $\left(\frac{9}{10}\right)^\circ$, yielding the conversion.
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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.

 
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Drain Brain said:
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,
\[
30^g=30\cdot1^g= 30\cdot\left(\frac{9}{10}\right)^\circ =27^\circ.
\]
 
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