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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