The following number is a BASE-5 NUMBER. Convert this to a base 10 number and enter your answer in the box.
124420

To convert the base-5 number \(124420_5\) to base-10, we need to expand it as follows:

\[
124420_5 = 1 \cdot 5^5 + 2 \cdot 5^4 + 4 \cdot 5^3 + 4 \cdot 5^2 + 2 \cdot 5^1 + 0 \cdot 5^0
\]

Now, calculating the powers of 5:

\[
5^5 = 3125, \quad 5^4 = 625, \quad 5^3 = 125, \quad 5^2 = 25, \quad 5^1 = 5, \quad 5^0 = 1
\]

Substitute these values into the expression:

\[
124420_5 = 1 \cdot 3125 + 2 \cdot 625 + 4 \cdot 125 + 4 \cdot 25 + 2 \cdot 5 + 0 \cdot 1
\]

\[
= 3125 + 1250 + 500 + 100 + 10 + 0
\]

Now, sum the terms:

\[
3125 + 1250 + 500 + 100 + 10 = 4985
\]

So, \(124420_5 = 4985_{10}\).

Would you like more details or have any questions?

Here are some related questions:

1. How do you convert a base-7 number to base-10?
2. Can you convert \(32014_5\) to base-10?
3. What is \(4985_{10}\) in base-5?
4. How do you convert base-10 numbers to any other base?
5. How does place value work in different numeral systems?

**Tip:** When converting between bases, always start with the highest power and work your way down.

Learn how to convert the base-5 number 124420 to a base-10 number with a step-by-step solution. This problem involves the key concepts of base conversion and place value, suitable for students in Grades 6-8.

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