Convert 489 in base 10 to octal.
Understand the Problem
The question asks to convert the base-10 number 489 into its octal (base-8) representation. This involves successively dividing the decimal number by 8 and recording the remainders, which are then read in reverse order to obtain the octal equivalent.
Answer
$751_8$
Answer for screen readers
$489_{10} = 751_8$
Steps to Solve
- Divide 489 by 8
Divide 489 by 8 to get the quotient and remainder:
$489 \div 8 = 61$ with a remainder of $1$.
- Divide 61 by 8
Divide 61 by 8 to get the quotient and remainder:
$61 \div 8 = 7$ with a remainder of $5$.
- Divide 7 by 8
Divide 7 by 8 to get the quotient and remainder:
$7 \div 8 = 0$ with a remainder of $7$.
- Collect the remainders in reverse order
The remainders are 1, 5, and 7. Reading them in reverse order gives 751.
$489_{10} = 751_8$
More Information
Octal is a base-8 number system, using digits 0 to 7. It was historically popular in computing because it is a power of 2 (specifically, $2^3$), making it easy to convert between binary and octal. Each octal digit corresponds to three binary digits.
Tips
A common mistake is to not perform the divisions until the quotient is 0. Another mistake is to write the remainders in the wrong order. Be sure to read the remainders from bottom to top to get the correct octal number.
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