559
,
819
  is a BASE- 
12
  number.

Convert this to a BASE- 
10
  number and enter your answer in the box.

To convert the base-12 number \(559_{12}\) and \(819_{12}\) into base-10, we need to expand them using their place values based on base-12. Here's how:

1. **Convert \(559_{12}\):**

The digits represent powers of 12, starting from the right:

\[
559_{12} = 5 \cdot 12^2 + 5 \cdot 12^1 + 9 \cdot 12^0
\]

Calculating each term:

\[
5 \cdot 12^2 = 5 \cdot 144 = 720
\]
\[
5 \cdot 12^1 = 5 \cdot 12 = 60
\]
\[
9 \cdot 12^0 = 9 \cdot 1 = 9
\]

Summing these:

\[
720 + 60 + 9 = 789
\]

So, \(559_{12} = 789_{10}\).

2. **Convert \(819_{12}\):**

\[
819_{12} = 8 \cdot 12^2 + 1 \cdot 12^1 + 9 \cdot 12^0
\]

Calculating each term:

\[
8 \cdot 12^2 = 8 \cdot 144 = 1152
\]
\[
1 \cdot 12^1 = 1 \cdot 12 = 12
\]
\[
9 \cdot 12^0 = 9 \cdot 1 = 9
\]

Summing these:

\[
1152 + 12 + 9 = 1173
\]

So, \(819_{12} = 1173_{10}\).

### Final Answer:
- \(559_{12} = 789_{10}\)
- \(819_{12} = 1173_{10}\)

Let me know if you want details or have questions! Here are 5 questions for practice:

1. Convert \(ABC_{12}\) (where \(A = 10\), \(B = 11\), \(C = 12\)) to base-10.
2. How do you convert a base-10 number to base-12?
3. What is the base-10 equivalent of \(34A_{12}\) where \(A = 10\)?
4. What is the highest digit possible in a base-12 system?
5. How does place value work in any positional numeral system?

**Tip:** When converting from any base to base-10, use powers of that base, starting from the rightmost digit.

559, 819 is a BASE-12 number. Convert this to a BASE-10 number and enter your answer in the box.

Learn how to convert the base-12 numbers 559 and 819 into base-10 using step-by-step calculations. This problem covers key concepts in number systems, including positional notation and base conversion formulas. Suitable for students in Grades 8-10.

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