# $R^2$ of 1 but RMSE > 0

I am running k-fold cross validation on my training data, and then choosing the best set of hyper parameters, re-training on the training data and testing on a new (unseen) testing data. I am getting the following testing results (results on the unseen data):

R^2: 1.000

Can $$R^2$$ have a value of 1.00 but RMSE have a value of 0.081? Doesn't an $$R^2$$ of value 1 indicate no errors at all?
The $$R^2$$ value is rounded to 3 decimal places. If the exact $$R^2$$ is $$\ge$$0.9995, it would then be reported as 1.000.