Questions: Write 922 in the base-five system. 922=□(five )

Transcript text: Write 922 in the base-five system. \[ 922=\square_{\text {five }} \]

Solution

Solution Steps

To convert the number 922 from base ten to base five, we repeatedly divide the number by 5 and record the remainders. The remainders, read in reverse order, give the digits of the number in base five.

Step 1: Division by Base

To convert \( 922 \) from base ten to base five, we perform repeated division by \( 5 \) and keep track of the remainders.

Step 2: Calculate Remainders

\( 922 \div 5 = 184 \) with a remainder of \( 2 \)
\( 184 \div 5 = 36 \) with a remainder of \( 4 \)
\( 36 \div 5 = 7 \) with a remainder of \( 1 \)
\( 7 \div 5 = 1 \) with a remainder of \( 2 \)
\( 1 \div 5 = 0 \) with a remainder of \( 1 \)

Step 3: Construct Base Five Representation

Reading the remainders from bottom to top, we find that \( 922 \) in base five is represented as \( 12142 \).

Final Answer

Thus, the conversion of \( 922 \) to base five is given by \\(\boxed{12142}\\).

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