Degrees to Grades conversion conceptual doubt

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I was reading Loney's book on Trigonometry and had this one doubt. Loney says

Since a right angle is equal to 90° and also to 100 g , we have 90° = 100 g . 1 degree = 10/9 grades and 1 grade = 9/10 degress

Hence, to change degrees into grades, add on one- ninth; to change grades into degrees, subtract one-tenth.

I don't get how he derives the fact that we have to add one ninth or subtract one tenth from the above? My 15 year old brain can''t make sense of it.

Could you please explain how he derives the statement in bold from the above thanks.

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Check that $1-1/10=9/10$ and $1+1/9=10/9$ .. Now do you get it?