To convert the decimal number 175 into base 4, follow these steps:

1. Divide the number by 4 and record the remainder.
2. Use the quotient for the next division by 4, and repeat the process until the quotient is zero.
3. The base-4 number is then the remainders read from bottom to top.

Let's do the conversion for 175.

$175 \div 4 = 43 \text{ remainder } 3$ $43 \div 4 = 10 \text{ remainder } 3$ $10 \div 4 = 2 \text{ remainder } 2$ $2 \div 4 = 0 \text{ remainder } 2$

Reading the remainders from bottom to top, 175 in base-10 is equal to 2233 in base-4.

Would you like more details on the process or have any other questions?

Here are 5 related questions for further exploration:

1. How do you convert a number from base-4 back to base-10?
2. Can you convert 256 from base-10 to base-4?
3. What is the significance of different number bases in computer science?
4. How do you perform addition and subtraction in base-4?
5. What is the binary (base-2) equivalent of the number 175?

Tip: When converting numbers between different bases, practice with small numbers to strengthen your understanding before moving to larger numbers.