Question

a student performs the following computation in base five.
3
3 4_five
× 4_five
3 0 1_five
explain the meaning of the 3 above the 3.
the student multiplied the (4_five 4_five = 31_five or 31_five ones) and the 3 over the 3 represents the 3 from the regrouping of 31_five as 3 10_five + 1_five.

Explanation:

Step1: Analyze base - five multiplication

In base - five, when we multiply $4_{five}\times4_{five}$, we calculate $4\times4 = 16$ in base - ten. Converting 16 to base - five gives $31_{five}$ since $16=3\times5 + 1$.

Step2: Understand place - value in base - five

In base - five, the number $31_{five}$ can be written as $3\times5^1+1\times5^0$. The digit 3 in $31_{five}$ represents the number of fives.

Answer:

The first blank: ones; The second blank: fives