Question

The value of $ {45^0} $ in centesimal system is _____
(A) $ {25^g} $
(B) $ {50^g} $
(C) $ {75^g} $
(D) $ {100^g} $

Answer 1

Hint: Centesimal system is a system of angular measure where ninety degrees is equal to hundred centesimal degrees. Use this relation to calculate the value of \[{45^0}\]. Centesimal units can also be expressed in minutes and seconds.

Complete step-by-step answer:
In the centesimal system as well, degree measure is given in degree, minute and seconds. Where, ninety degrees is equal to hundred centesimal degrees. One centesimal degree is equal to hundred centesimal minutes and one centesimal minute is equal to hundred centesimal seconds.
Centesimal system is a system where ninety degrees is equal to hundred centesimal degrees. A centesimal degree is denoted by $ ^g $ .
Mathematically, we can write the relation between degrees and centesimal degrees as
 $ \Rightarrow {90^0} = {100^g} $
Now, if we divide both the sides by 2 we get
 $ \Rightarrow {45^0} = {50^g} $
Therefore, from the above explanation, the correct answer is, option (B) $ {50^g} $
So, the correct answer is “Option B”.

Note: The key point in this question was knowing what the centesimal system of units is. If you don’t know that, then there is no way to solve this question. So we need to have the idea of all the systems that we use for any measurement. And you also need to know the relationship between any two systems of units. Just like in this question, knowing the relationship between the degree measure and centesimal degree measure made the question really easy. There are other measures of angle as well. For example, radian measure. Where, $ 1radian = {180^0} $