Convert 529 in base 10 to a base 5 number

Convert 529 in base 10 to a base 5 number.

The correct answer and explanation is:

To convert the decimal number 529 into base 5, you need to divide the number by 5 repeatedly, recording the remainder each time. Here is the step-by-step process:

1. Divide 529 by 5:
   • 529 ÷ 5 = 105, remainder 4.
     The remainder is 4, so the rightmost digit of the base 5 number is 4.
2. Divide 105 by 5:
   • 105 ÷ 5 = 21, remainder 0.
     The remainder is 0, so the next digit of the base 5 number is 0.
3. Divide 21 by 5:
   • 21 ÷ 5 = 4, remainder 1.
     The remainder is 1, so the next digit of the base 5 number is 1.
4. Divide 4 by 5:
   • 4 ÷ 5 = 0, remainder 4.
     The remainder is 4, so the leftmost digit of the base 5 number is 4.

Now, you collect the remainders from bottom to top: 4104.

Thus, the base 5 representation of 529 is 4104.

Explanation

When converting a number from base 10 to another base, such as base 5, the method involves repeatedly dividing the number by the base and recording the remainders. The remainders represent the digits of the base 5 number, starting from the least significant (rightmost) digit.

In this case, dividing 529 by 5 step by step gave us remainders of 4, 0, 1, and 4. The final base 5 number is written by arranging the remainders from bottom to top, yielding 4104.

This method works because in any base, the remainder when dividing by the base gives the correct place value for each digit in the base number system. The division continues until the quotient becomes zero, at which point you have all the digits of the base number.

The base 5 number system uses digits from 0 to 4. As you can see from the result, the base 5 representation of 529 only involves the digits 4, 1, and 0, confirming it fits within the constraints of base 5.