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If the recipe calls for 3 tablespoons of kernels and she uses 10 tablespoons, then she is using 10/3 = <<10/3=3.33>>3.33 times the amount of kernels required.
The recipe calls for 1/2 a cup of butter, and she is using 3.33 times the amount of kernels required, so she needs 1/2 * 3.33 = <<1/2*3.33=1.665>>1.665 cups of butter.
Since the answer needs to be rounded to the nearest hundredths, then she needs 1.665 rounded to the nearest hundredths = <<1.665=1.67>>1.67 cups of butter. Answer: \boxed{1.67}.