How would i convert base8 number of 725 to a base7 number?
The easiest way I know is to convert the base 8 number to base 10, then convert the base 10 number to base 7.
$\displaystyle 725_8 = 7 \cdot 8^2 + 2 \cdot 8^1 + 5 \cdot 8^0 = 469$
where the 469 is in base 10.
Now to convert 469 to base 7. The largest power of 7 that divides 469 (without being larger than it) is 3:
$\displaystyle 469 = 1 \cdot 7^3 + 126$
The next largest power of 7 is 2:
$\displaystyle 469 = 1 \cdot 7^3 + 2 \cdot 7^2 + 28$
The next largest power of 7 is 1:
$\displaystyle 469 = 1 \cdot 7^3 + 2 \cdot 7^2 + 4 \cdot 7^1 + 0$
And the last power of 7 is 0:
$\displaystyle 469 = 1 \cdot 7^3 + 2 \cdot 7^2 + 4 \cdot 7^1 + 0 \cdot 7^0$
So $\displaystyle 725_8 = 469_{10} = 1240_7$
I would not be surprised to find that the Euclidean Algorithm provides a way to do this directly from base 8 to base 7, but I don't know how to set it up.
-Dan
Hello, Edbaseball17!
How would i convert $\displaystyle 725_8$ to a base 7 number?
Convert to base-ten: .$\displaystyle 725_8 \:=\:469_{10}$
Then convert to base-seven: .$\displaystyle 469_{10} \:=\:1240_7$
I trust you know the necessary procedures.
Otherwise, you shouldn't have been assigned this problem.
.
Hello, Edbaseball17!
I was trying to go directly from base 8 to base 7.
This can be done IF you can divide in base 8 . . .
$\displaystyle \begin{array}{cccccc} & & 1 & 0 & 3 \\
& & -- & -- & -- \\ 7 & ) & 7 & 2 & 5 \\ & & 7 \\
& & --& -- \\
& & & 2 & 5\\
& & & 2 & 5 \\
& & & --& -- \\
& & & & 0
\end{array}$ . . Remainder: 0
. . $\displaystyle \begin{array}{cccccc}& & & 1 & 1 \\
& & -- & -- & --\\
7 & ) & 1 & 0 & 3 \\
& & & 7 \\
& & & -- \\
& & & 1 & 3 \\
& & & & 7 \\
& & & --& -- \\
& & & & 4 \end{array}$ . . Remainder: 4
. . . . $\displaystyle \begin{array}{cccccc} & & & 1 \\
& & -- & -- \\
7 & ) & 1 & 1 \\
& & & 7 \\
& & -- & -- \\
& & & 2 \end{array}$ . . Remainder: 2
. . . . . . $\displaystyle \begin{array}{cccccc}& & 0 \\
& & -- \\
7 & ) & 1 \\
& & 0 \\
& & -- \\
& & 1 \end{array}$ . . Remainder: 1
Therefore: .$\displaystyle \boxed{\;725_8 \;=\;1240_7\;}$