To determine how many 4-digit numbers are multiples of 5, let's break it down systematically:

Step 1: Characteristics of 4-digit numbers

• A 4-digit number ranges from 1000 to 9999.
• To be a multiple of 5, the number must end in either 0 or 5.

Step 2: Counting the numbers

• For the last digit, there are 2 choices: 0 or 5.
• For the first digit, which cannot be 0 (to keep it a 4-digit number), there are 9 choices: 1 through 9.
• For the second and third digits, there are no restrictions, so each can be any digit (0 through 9), giving 10 choices each.

Step 3: Total combinations

The total number of 4-digit numbers that are multiples of 5 is: $\text{Total} = (\text{choices for first digit}) \times (\text{choices for second digit}) \times (\text{choices for third digit}) \times (\text{choices for last digit})$ $\text{Total} = 9 \times 10 \times 10 \times 2 = 1800$

Final Answer:

There are 1,800 four-digit numbers that are multiples of 5.

Would you like a detailed explanation of any step?

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Here are 5 related questions to expand your understanding:

1. How many 4-digit numbers are multiples of 10?
2. How many 4-digit numbers are divisible by 3 but not by 5?
3. How many 4-digit numbers are divisible by both 2 and 5?
4. How many 4-digit numbers have distinct digits and are multiples of 5?
5. How many 5-digit numbers are multiples of 5?

Tip: Always check the divisibility rule when determining if a number is a multiple of 5, which is based solely on its last digit (0 or 5).