Questions: Write 250 nine in the base-ten system.

Transcript text: Write 250 nine in the base-ten system.

Solution

Solution Steps

Step 1: Convert Base-Nine to Base-Ten

To convert the base-nine number \( 250_{\text{nine}} \) to base-ten, we use the formula: \[ 250_{\text{nine}} = 2 \cdot 9^2 + 5 \cdot 9^1 + 0 \cdot 9^0 \] Calculating each term:

\( 2 \cdot 9^2 = 2 \cdot 81 = 162 \)
\( 5 \cdot 9^1 = 5 \cdot 9 = 45 \)
\( 0 \cdot 9^0 = 0 \)

Now, we sum these values: \[ 162 + 45 + 0 = 207 \]

Final Answer

The base-ten equivalent of \( 250_{\text{nine}} \) is \\(\boxed{207}\\).

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