Questions: Write 38 in the base-nine system in the base-ten system. 38 in the base-nine system =

Write 38 in the base-nine system in the base-ten system.
38 in the base-nine system =
Transcript text: Write $38_{\text {nine }}$ in the base-ten system. \[ 38_{\text {nine }}= \]
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Solution

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Solution Steps

Step 1: Understand the Problem

We are given the number 38nine38_{\text{nine}}, which is in base nine. Our goal is to convert this number to the base-ten system.

Step 2: Break Down the Number

In base nine, the number 38nine38_{\text{nine}} can be expanded as: 3×91+8×90 3 \times 9^1 + 8 \times 9^0

Step 3: Calculate Each Term

Calculate the value of each term: 3×91=3×9=27 3 \times 9^1 = 3 \times 9 = 27 8×90=8×1=8 8 \times 9^0 = 8 \times 1 = 8

Step 4: Sum the Terms

Add the results of the two terms: 27+8=35 27 + 8 = 35

Final Answer

35 \boxed{35}

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