Two-digit natural numbers are formed, with replacement, from the digits 0 through 9.

How many numbers are greater than 54?
 numbers

To determine how many two-digit natural numbers formed from the digits 0 through 9 are greater than 54, we can break down the problem as follows:

### Step 1: Define the range of two-digit numbers
- The two-digit numbers range from 10 to 99.

### Step 2: Identify numbers greater than 54
- We need to count the numbers from 55 to 99 (inclusive) because these are the numbers greater than 54.

### Step 3: Count the numbers in this range
- The smallest number in this range is 55, and the largest is 99.
- To find the total count of numbers from 55 to 99, use the formula for the number of terms in an arithmetic sequence:
  \[
  \text{Number of terms} = \text{Last term} - \text{First term} + 1
  \]
  \[
  \text{Number of terms} = 99 - 55 + 1 = 45
  \]

### Final Answer:
There are **45** two-digit natural numbers greater than 54.

Would you like more details or have any questions?

Here are some related questions to explore further:

1. How many two-digit numbers are less than or equal to 54?
2. What is the probability of randomly selecting a number greater than 54 from the set of all two-digit numbers?
3. How many two-digit numbers are divisible by 5 and greater than 54?
4. If you form three-digit numbers instead, how many of them are greater than 554?
5. How does the count change if the digits cannot be repeated?

**Tip:** When dealing with ranges of numbers, counting the terms using the arithmetic sequence formula can simplify the process.

Learn how to count the number of two-digit natural numbers greater than 54 using arithmetic sequences. This problem involves identifying the range of numbers and applying the formula for counting terms in an arithmetic sequence. Suitable for students in Grades 6-8.

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