Write 

21

 in the base-three system.



To convert \(21\) from base-ten (decimal) to base-three:

1. Find the largest power of 3 less than or equal to \(21\).

\[
3^2 = 9 \quad (\text{since } 3^3 = 27 \text{ is too large})
\]

2. Divide \(21\) by \(9\):

\[
21 \div 9 = 2 \quad (\text{remainder } 3)
\]

3. Now divide the remainder \(3\) by \(3^1 = 3\):

\[
3 \div 3 = 1 \quad (\text{remainder } 0)
\]

4. Finally, for \(3^0 = 1\), the remainder is already \(0\), so no further division is needed.

So, \(21\) in base-three is written as \(210_3\).

Would you like more details on the conversion process or any other questions?

Here are 5 related questions:
1. How do you convert larger numbers to base-three?
2. What is the base-three representation of \(45\)?
3. How do you convert a base-three number back to base-ten?
4. What is the base-three equivalent of the decimal number \(100\)?
5. How do you perform addition in the base-three system?

**Tip:** To check your conversion from decimal to another base, convert it back to decimal to verify your answer!

Learn how to convert the decimal number 21 to its base-three equivalent with a detailed, step-by-step explanation. This problem involves base conversions, using the division method. Ideal for students in Grades 5-7.

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