Decimal to Octal

Decimal Number: A decimal number is a base-ten numeral system where each digit can be any of the ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. It represents quantities using powers of 10.

Decimal Number Example: For instance, the number 5432 is a decimal number where 5 is in the thousands place, 4 is in the hundreds place, 3 is in the tens place, and 2 is in the ones place.

Octal Number: An octal number is a base-eight numeral system that uses eight symbols: 0, 1, 2, 3, 4, 5, 6, and 7. It represents quantities using powers of 8.

Octal Number Example: Consider the octal number 427. In this number, 4 is in the 64s place (8^2), 2 is in the 8s place (8^1), and 7 is in the ones place (8^0). When converted to decimal, this octal number represents the decimal number 287.

Conversion Process: Decimal to Octal

1. Divide by 8: Start by dividing the decimal number by 8.
2. Record Remainders: Keep track of the remainder (which can range from 0 to 7) after each division. These remainders will form the octal digits.
3. Continue Division: Repeat the division process with the quotient until it becomes 0.
4. Reverse the Remainders: After all divisions, reverse the sequence of remainders to obtain the octal representation of the decimal number.

Example: Convert Decimal 175 to Octal

Step 1: $\frac{175}{8} = 21$ Remainder 7
Step 2: $\frac{21}{8} = 2$ Remainder 5
Step 3: $\frac{2}{8} = 0$ Remainder 2

Reversing the remainders, we get 257. Therefore, the octal representation of decimal number 175 is 257.