Sure, let's convert the decimal number [tex]\(437_{10}\)[/tex] to its equivalent in base 8 (octal).
### Step-by-Step Conversion:
1. Understanding the Process:
- Converting a decimal number to an octal number involves dividing the decimal number by 8 repeatedly and keeping track of the remainders.
2. Start with the Decimal Number:
- The given decimal number is 437.
3. Repeat the Division:
- Divide the number by 8 and record the quotient and remainder.
- First division: [tex]\(437 \div 8 = 54\)[/tex] with a remainder of [tex]\(5\)[/tex].
- Quotient: 54
- Remainder: 5
- Second division: [tex]\(54 \div 8 = 6\)[/tex] with a remainder of [tex]\(6\)[/tex].
- Quotient: 6
- Remainder: 6
- Third division: [tex]\(6 \div 8 = 0\)[/tex] with a remainder of [tex]\(6\)[/tex].
- Quotient: 0
- Remainder: 6
4. Read the Remainders from Bottom to Top:
- The remainders, read from bottom to top, give us the octal number: [tex]\(665\)[/tex].
### Conclusion:
So, the conversion of [tex]\(437_{10}\)[/tex] to base 8 (octal) is:
[tex]\[
437_{10} = 665_8
\][/tex]
This means that the decimal number 437 is equal to 665 in octal.
