Write the number in expanded notation.
64500013eight

To write the number **64500013₈** (in base 8) in expanded notation, we break down each digit according to its place value in base 8:

**64500013₈** can be expanded as:

\[
6 \cdot 8^7 + 4 \cdot 8^6 + 5 \cdot 8^5 + 0 \cdot 8^4 + 0 \cdot 8^3 + 0 \cdot 8^2 + 1 \cdot 8^1 + 3 \cdot 8^0
\]

Now, let’s calculate the powers of 8 and multiply them by the corresponding digits:

\[
6 \cdot 2097152 + 4 \cdot 262144 + 5 \cdot 32768 + 0 \cdot 4096 + 0 \cdot 512 + 0 \cdot 64 + 1 \cdot 8 + 3 \cdot 1
\]

\[
= 12582912 + 1048576 + 163840 + 0 + 0 + 0 + 8 + 3
\]

\[
= 13735339
\]

So, **64500013₈** in expanded form is:

\[
6 \cdot 8^7 + 4 \cdot 8^6 + 5 \cdot 8^5 + 0 \cdot 8^4 + 0 \cdot 8^3 + 0 \cdot 8^2 + 1 \cdot 8^1 + 3 \cdot 8^0 = 13735339
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you convert a base-8 number to base-10?
2. What is the expanded notation of 72543₈?
3. How does place value work in base-8 systems?
4. Can you convert 64500013₈ back to its decimal form step-by-step?
5. What would be the binary representation of 64500013₈?

**Tip:** When converting between bases, always pay attention to the place value of each digit according to the base being used.

Write the number in expanded notation. 64500013₈

Learn how to write the base-8 number 64500013₈ in expanded notation. This step-by-step solution breaks down the place value in base-8 and converts it into base-10, showing key concepts such as place value and expanded notation for different number systems.

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