Question

387 in base 10 to base 5

Answer 1

3022

Explanation:

To convert a number from base 10 to base 5, divide the number repeatedly by 5, keeping track of each remainder, until you get a quotient that is equal to zero

`\begin{array}{rcccc}\textbf{Division} & = & \textbf{quotient} & +& \textbf{remainder}\\387 / 5 & = & 77 & + & \mathbf{2} \\77 / 5 & = & 15 & + & \mathbf{2} \\15 / 5 & = &3 & + & \mathbf{0} \\3 / 5 & = & 0 & + & \mathbf{3} \\\end{array}`

Next, write all the remainders in reverse order.

387₁₀ = 3022₅

Check:

387 = 3×5³ + 0×5² + 2×5¹ + 2×5⁰

387 = 3×125 + 0×25 + 2×5 + 2×1

387 = 375 + 0 + 10 + 2

387 = 387

OK.

Answer 2

Answer: 387 in base 10 to base 5 is 3022

Explanation:

To convert 387 in base 10 to base 5, we would take the following steps

Firstly , we would divide the number to be converted by 5. The remainder forms the last digit of the number in base 5 while the quotient is divided again to get a new quotient and remainder. The new remainder forms the next digit to the left of the last digit. It continues till it gets to zero. Therefore,

387/5 = 77 remainder 2(last digit)

77/5 = 15 remainder 2(next digit to the left of the last).

15/5 = 3 remainder 0(next digit to the left)

3/5 = 0 remainder 3(next and final digit to the left)

Therefore, 387 in base 10 to base 5 is 3022