What is the octal equivalent of the decimal number 417?
Understand the Problem
The question is asking for the octal representation of the decimal number 417. To convert from decimal to octal, we can repeatedly divide the decimal number by 8 and record the remainders, which will give us the digits of the octal number in reverse order.
Answer
$641_8$
Answer for screen readers
The octal representation of the decimal number 417 is $641_8$.
Steps to Solve
-
Divide the decimal number by 8
Start with the decimal number 417 and divide it by 8.
$$ 417 \div 8 = 52 \quad \text{(integer part)} $$
Record the remainder:
$$
417 \mod 8 = 1
$$
-
Repeat the process with the quotient
Now take the quotient from the previous division, which is 52, and divide it by 8.
$$ 52 \div 8 = 6 \quad \text{(integer part)} $$
Record the remainder:
$$
52 \mod 8 = 4
$$
-
Continue until the quotient is zero
Next, take the quotient 6 and divide it by 8.
$$ 6 \div 8 = 0 \quad \text{(integer part)} $$
Record the remainder:
$$
6 \mod 8 = 6
$$
Now we can stop since the quotient is 0.
-
Read the remainders in reverse order
Now, compile the remainders from the last division to the first:
$$ 6, 4, 1 $$
Thus, the octal representation of the decimal number 417 is $641_8$.
The octal representation of the decimal number 417 is $641_8$.
More Information
When converting from decimal to octal, remember that octal is base 8. Each digit in an octal number can only be between 0 to 7. The process of repeatedly dividing by 8 allows you to uncover each digit of the octal number.
Tips
- Forgetting to record remainders: Make sure to always note the remainder for each division step.
- Reading the remainders in the wrong order: Remember to read the remainders from the last division to the first.
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