In the left column, I have an ordinal integer field. In the right column, I have a scaled float feature.
Should I scale the ordinal field since it is getting so much bigger than the other feature?
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We scale data because certain algorithm will not work optimally esp. Gradient descent. You may check the internet for further detail.
Coming to the exact question -
I am assuming, you have done the analysis that the Oridinal feature will be used as a Continuous(Not Categorical) feature with its respective values. So, I will ignore this point
Models don't see the feature scale, it looks for the respective variance, interaction with other features, Correlation with the target etc.(in a very simple language) and scaling will not hamper these parameters.
So, you must scale if that is your only concern.
You may ignore it for some Models e.g. Decision Tree/RF will work fine even without scaling.