## What Are Signed Numbers? **Signed numbers** are numbers that have either a **positive (+)** or **negative (−)** sign in front of them. These are used to indicate **direction**, **gain vs. loss**, or **increase vs. decrease**. In electrical systems, signed numbers are common when working with: - **Voltage rise and drop** (e.g. +12 V, −5 V) - **Current flow direction** (positive vs. reverse current) - **Temperature rise/fall** during diagnostics - **Power gain/loss** in a circuit or system ### Number Line Overview A **number line** helps visualize signed numbers. Zero is the center, with positive numbers extending to the right and negative numbers to the left. Example: ``` <--- −3 −2 −1 0 +1 +2 +3 ---> ``` This is useful when you want to think of signed numbers as **position or movement**. For example, starting at 0 and moving −3 units is going 3 units **left**. ## Positive vs. Negative in Real Life Electrical Work |Situation|Example|Signed Number| |---|---|---| |Voltage drop from a source|−2.5 V|Negative| |Voltage increase across a boost converter|+3.6 V|Positive| |Net power loss in a system|−15 W|Negative| |Phase lead (ahead in time)|+30°|Positive| |Phase lag (behind in time)|−30°|Negative| ## Absolute Value The **absolute value** of a number is its **distance from zero**, regardless of direction. It is always positive. Notation: $|\text{number}|$ Examples: $|-5| = 5$ $|+7| = 7$ $|0| = 0$ In electrical troubleshooting, absolute value is used when only the **magnitude** of voltage or current matters, not the direction. Example: If a meter reads −6.2 V, the absolute value is 6.2 V. This helps you determine if the voltage level is within the acceptable range, even if the polarity is reversed. ## Summary - Signed numbers include **positive** and **negative** values. - They are common in electrical work for voltage, current, phase, and temperature. - A **number line** helps visualize movement or change in value. - The **absolute value** tells you the magnitude of a number, ignoring the sign.