Explain how you can determine whether a number is an integer. List examples of integers and non-integers

To determine whether a number is an integer, you need to check if it is a whole number without any fractional or decimal part. In other words, an integer is a number that can be written without a fractional or decimal component, and it can be positive, negative, or zero.

### Steps to Determine if a Number is an Integer:
1. **Check for Decimals or Fractions:** If the number has a decimal point with digits following it (e.g., 3.14) or is written as a fraction (e.g., 1/2), it is not an integer.
2. **Whole Number Requirement:** The number must be a whole number. This means it has to be a complete countable number like -3, 0, or 7.
3. **No Mixed Numbers:** Mixed numbers (e.g., 2 1/2) are not integers because they include a fraction part.
4. **Division by 1 Test:** If a number can be divided by 1 without leaving a remainder, it is an integer. For example, 6 ÷ 1 = 6 (an integer), but 6.5 ÷ 1 = 6.5 (not an integer).

### Examples of Integers:
- **Positive Integers:** 1, 2, 15, 100
- **Negative Integers:** -1, -7, -20, -1000
- **Zero:** 0 (zero is considered an integer)

### Examples of Non-Integers:
- **Decimals:** 3.14, 0.5, -2.75
- **Fractions:** 1/2, 3/4, -5/8
- **Mixed Numbers:** 2 1/2, -3 1/3

### Summary
- **Integers** are whole numbers without fractions or decimals.
- **Non-Integers** include decimals, fractions, and mixed numbers.

Would you like more details or have any questions?

### Related Questions:
1. How can you convert a decimal or fraction into an integer?
2. What is the difference between a rational number and an integer?
3. How do you determine if a number is a rational number?
4. What are the properties of integers in mathematical operations?
5. How do you classify numbers into natural numbers, whole numbers, and integers?

### Tip:
Remember that all integers are rational numbers, but not all rational numbers are integers.

Explore the concept of integers: what they are, examples of integers versus non-integers, and their properties. Learn how to determine if a number is an integer with clear examples and explanations.

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