Integers provide a straightforward way to represent data that involves whole units, especially when dealing with values relative to a baseline of zero.
According to the definition, positive whole numbers, their opposites, and zero are called integers. This set of numbers includes positive integers (like 1, 2, 3...), negative integers (like -1, -2, -3...), and zero (0).
Representing Different Data Values
Integers are particularly useful for showing magnitude and direction relative to a starting point or zero value.
- Positive Integers: Data that are greater than zero are represented by positive integers. These numbers indicate an increase, a value above a baseline, or a gain. A positive integer can be written with or without a
+sign (e.g., +5 is the same as 5). - Negative Integers: As the reference states, to represent data that are less than a 0, you can use negative integers. A negative integer is written with a
-sign. These numbers are used to show a decrease, a value below a baseline, a loss, or the opposite direction of a positive value. For example, -10 represents ten units less than zero. - Zero (0): Zero represents the baseline, no change, or a neutral value. It is the integer that is neither positive nor negative.
Practical Examples of Integer Data
Integers are commonly used across various fields to represent data clearly. Here are some examples:
- Temperature: Degrees above zero are positive (e.g., 20°C), degrees below zero are negative (e.g., -5°C), and 0°C is the freezing point of water.
- Finance: A profit is represented by a positive integer (e.g., $500 profit = +500), a loss by a negative integer (e.g., $200 loss = -200), and breaking even by zero ($0 change = 0).
- Altitude: Heights above sea level are positive (e.g., 100 meters above sea level = +100), depths below sea level are negative (e.g., 50 meters below sea level = -50), and sea level itself is zero (0 meters).
- Sports: A score change can be represented by integers. Gaining points uses positive integers, losing points uses negative integers, and no score change is zero.
Consider the following table illustrating how different data scenarios can be represented using integers:
| Data Description | Integer Representation | Meaning Relative to Zero |
|---|---|---|
| A gain of 10 points | +10 or 10 | Ten units more than zero (a positive change) |
| A drop of 7 degrees | -7 | Seven units less than zero (a decrease from the baseline) |
| No change in balance | 0 | Exactly at the zero baseline (no difference) |
| 25 feet below the surface | -25 | Twenty-five units less than the zero surface level |
By using positive integers for values greater than zero and negative integers for values less than zero, along with zero for the baseline, integers provide a simple and effective system for representing data that involves whole units and direction relative to a central point.
