why were you unable to use non-integer numbers (like ½ or 0.43) for the coefficients in a balanced chemical equation?

Chemistry: Matter and Change
1st Edition
ISBN:9780078746376
Author:Dinah Zike, Laurel Dingrando, Nicholas Hainen, Cheryl Wistrom
Publisher:Dinah Zike, Laurel Dingrando, Nicholas Hainen, Cheryl Wistrom
Chapter9: Chemical Reactions
Section: Chapter Questions
Problem 58A
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  1.  why were you unable to use non-integer numbers (like ½ or 0.43) for the coefficients in a balanced chemical equation? 
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