Questions: 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. \[ 38_{\text {nine }}= \]

Solution

Step 1: Understand the Problem

We are given the number $38_{\text{nine}}$, 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 $38_{\text{nine}}$ can be expanded as: \[ 3 \times 9^1 + 8 \times 9^0 \]

Step 3: Calculate Each Term

Calculate the value of each term: \[ 3 \times 9^1 = 3 \times 9 = 27 \] \[ 8 \times 9^0 = 8 \times 1 = 8 \]

Step 4: Sum the Terms

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

\[ \boxed{35} \]

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