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The question asks to convert the number \( 110_3 \) (in base 3) to its base 10 equivalent.

Let's break this down:

### Step-by-step conversion of \( 110_3 \):
The base-3 number \( 110_3 \) can be expanded as:

\[
110_3 = 1 \times 3^2 + 1 \times 3^1 + 0 \times 3^0
\]

Now calculate each term:
- \( 1 \times 3^2 = 1 \times 9 = 9 \)
- \( 1 \times 3^1 = 1 \times 3 = 3 \)
- \( 0 \times 3^0 = 0 \times 1 = 0 \)

Adding these up:
\[
9 + 3 + 0 = 12
\]

Thus, \( 110_3 \) in base-10 is \( 12 \).

Would you like more details or explanations? Here are five related questions for practice:

1. Convert \( 210_3 \) to base 10.
2. Convert \( 102_3 \) to base 10.
3. How would you convert a number from base 10 to base 3?
4. What is \( 1201_3 \) in base 10?
5. Convert \( 222_3 \) to base 10.

**Tip:** When converting from any base to base 10, expand the number by multiplying each digit by the base raised to the power of its position (starting from 0 on the right).

Write 110 (in base 3) in the base-ten system.

This page explains how to convert the base-3 number 110 to its base-10 equivalent using a step-by-step method. The solution is suitable for students in grades 5-7, focusing on base conversion concepts and number systems.

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