We are given the number 38nine38_{\text{nine}}38nine, which is in base nine. Our goal is to convert this number to the base-ten system.
In base nine, the number 38nine38_{\text{nine}}38nine can be expanded as: 3×91+8×90 3 \times 9^1 + 8 \times 9^0 3×91+8×90
Calculate the value of each term: 3×91=3×9=27 3 \times 9^1 = 3 \times 9 = 27 3×91=3×9=27 8×90=8×1=8 8 \times 9^0 = 8 \times 1 = 8 8×90=8×1=8
Add the results of the two terms: 27+8=35 27 + 8 = 35 27+8=35
35 \boxed{35} 35
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