To convert the number $745_{10}$ (in base 10) to base 5, follow these steps:

Steps:

1. Divide the number by 5 and record the remainder.
   This remainder becomes the least significant digit (rightmost digit) in base 5.

2. Repeat the division with the quotient until the quotient becomes 0.
   Each remainder you obtain becomes the next digit in the base 5 representation (from right to left).

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Conversion:

1. $745 \div 5 = 149$ remainder 0
   (Least significant digit: $0$)

2. $149 \div 5 = 29$ remainder 4
   (Next digit: $4$)

3. $29 \div 5 = 5$ remainder 4
   (Next digit: $4$)

4. $5 \div 5 = 1$ remainder 0
   (Next digit: $0$)

5. $1 \div 5 = 0$ remainder 1
   (Most significant digit: $1$)

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Final Answer:

Reading the remainders from bottom to top, $745_{10}$ in base 5 is:

$745_{10} = 10440_5$

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Would you like more detailed explanations or examples? 😊

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Related Questions:

1. How do you convert numbers from other bases to base 10?
2. What is the general formula for converting between arbitrary bases?
3. Can you explain how to perform arithmetic (e.g., addition) in base 5?
4. What are some practical applications of base conversion?
5. How do you handle fractional numbers during base conversion?

Tip:

When converting to any base, always verify by converting back to ensure accuracy!