The short answer is no, pi/2 radians and 1.57 radians are not exactly the same thing - though they are close; pi is an irrational number, and as such has no exact decimal representation. Hence, neither does pi/2.

A degree is defined such that exactly 360 form a circle. 360...

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The short answer is no, pi/2 radians and 1.57 radians are not exactly the same thing - though they are close; pi is an irrational number, and as such has no exact decimal representation. Hence, neither does pi/2.

A degree is defined such that exactly 360 form a circle. 360 is a rational number, and can be divided by 4 to get exactly 90 -- one quarter of a circle.

A radian is defined based on the circumference of the circle. A radian is defined as the angle at which the length along the edge of the circle is equal to the radius of the circle. pi is the number of radians in one-half of the circle. You can take a string that is the length of the radius and wrap it on the top of the circle 3.14159265.... times.