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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.

Convert from 175, a base-10 number, to a base-4 number. Enter your result as a string of digits in the correct order with no spaces or commas.

Learn how to convert the decimal number 175 into its base-4 equivalent using the division and remainder method. This guide provides a detailed step-by-step explanation for converting between number systems, suitable for Grades 6-9.

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