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A three-digit number is an integer that ranges from 100 to 999. It consists of exactly three digits, which means it cannot start with a 0, as this would make it a two-digit number. Therefore, the first digit must be a non-zero number. That's why we start counting from 100 instead of 000. These numbers are pivotal in understanding the basics of place value, as each digit represents a different power of ten. The first digit is in the hundreds place, the second digit in the tens place, and the third digit in the units place.
Numbers like 123, 450, and 789 are examples of three-digit numbers. They demonstrate how we combine digits to form a comprehensive number. Understanding three-digit numbers is essential for learning larger multi-digit numbers and the fundamentals of number systems.

The multiplication rule is a fundamental principle in combinatorics used to find the total number of outcomes for a series of events. When multiple choices are involved, and each choice is independent of the others, the multiplication rule comes into play.
For example, if you have 9 options for the first event and 10 options for each of the second and third events, you can find the total number of possible combinations by multiplying these numbers together. In our case of three-digit numbers:

• 9 choices for the main digit (as it can't be 0)
• 10 choices for the second digit
• 10 choices for the third digit

Using the multiplication rule, the total count becomes: \[9 \times 10 \times 10 = 900\].
This shows us that there are 900 possible combinations for forming a three-digit number, where the choices for each position in the number are multiplied together to find the total.

When constructing numbers, digits serve as the building blocks. The digits 0 through 9 form the base of our number system, known as the decimal or base 10 system.
Each digit has a unique value and contributes differently based on its position in a number. For instance, the digit '5' in the hundreds place (as in the number 500) represents 500, whereas in the units place (as in the number 5), it represents just 5.
In the context of forming three-digit numbers, the digits from 1 to 9 can be used in the hundreds place, because using 0 would not meet the requirement of being a three-digit number. However, any digit from 0 to 9 can be in the tens or units place, providing the flexibility needed to reach the total of 900 different combinations.