Integers, fractions, and decimals are different ways to represent numbers.
Integers
- Definition: Integers are whole numbers (not fractions or decimals) and their negatives. They include zero.
- Examples: -3, -2, -1, 0, 1, 2, 3...
- Key Characteristics:
- No fractional or decimal parts.
- Can be positive, negative, or zero.
- Use Case: Counting objects, representing temperature below zero.
Fractions
- Definition: Fractions represent a part of a whole. They are expressed as a ratio of two integers: a numerator (top number) and a denominator (bottom number).
- Examples: 1/2, 3/4, 5/8, 10/3
- Key Characteristics:
- Represent values between whole numbers.
- Denominator cannot be zero.
- Types of Fractions:
- Proper Fraction: Numerator is smaller than the denominator (e.g., 1/2).
- Improper Fraction: Numerator is greater than or equal to the denominator (e.g., 5/4).
- Mixed Number: A whole number and a proper fraction combined (e.g., 1 1/4).
- Use Case: Representing proportions, dividing a pizza.
Decimals
- Definition: Decimals are another way to represent fractions. They are based on powers of ten.
- Examples: 0.5, 0.75, 3.14, 2.0
- Key Characteristics:
- Use a decimal point to separate the whole number part from the fractional part.
- Each digit to the right of the decimal point represents a fraction with a denominator that is a power of 10 (tenths, hundredths, thousandths, etc.).
- Types of Decimals:
- Terminating Decimal: Decimal that ends (e.g., 0.5).
- Repeating Decimal: Decimal that has a repeating pattern of digits (e.g., 0.333...).
- Relationship to Fractions: Every fraction can be represented as a decimal (either terminating or repeating) by dividing the numerator by the denominator.
- Use Case: Representing money, precise measurements.
In summary, integers are whole numbers, fractions represent parts of a whole as a ratio, and decimals represent parts of a whole using powers of ten. They are all different ways to express numerical values, each with its own strengths and applications.
