Find the number of real solutions of the equation
\[\frac{x}{100} = \sin x.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the number of real solutions of the equation
\[\frac{x}{100} = \sin x.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
63
Find the number of real solutions of the equation
\[\frac{x}{100} = \sin x.\]
train