Acentimeter is __ meter(s). 1,000 100 1/100th 1/1,000th

A centimetre is 1/100th of a metre, because there is 100 centimetres in a metre

It's 1/100 since 1 m = 100 cm.
 
1/100 is the inverse of the conversion factor. 

For example, if you had to convert 50 m to cm, you would multiply 50 by 100 (1 m = 100 cm). 
 
But to convert 50 cm to m, you would have to divide 50 by 100. So, 1 cm to m is 1/100.