Magnitude Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Magnitude.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Magnitude measures the size or length of a quantity — for a vector (a, b), it is sqrt(a^2 + b^2). For a single number, magnitude is its absolute value: how far it is from zero, ignoring sign or direction.

How big something is, regardless of which way it points—5 miles east and 5 miles west are the same distance.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Magnitude measures size without direction—the 'unsigned' version of a number.

Common stuck point: Thinking -10 is 'less' than 5 in every sense (position yes, magnitude no).

Sense of Study hint: Ask yourself: how far is this number from zero on the number line? Ignore which side of zero it's on — just measure the distance.

Worked Examples

Example 1

easy
Find the magnitude (absolute value) of each: |{-9}|, |7|, |0|.

Solution

  1. 1
    |-9| = 9 because -9 is 9 units from zero on the number line.
  2. 2
    |7| = 7 because 7 is already 7 units from zero (positive, so unchanged).
  3. 3
    |0| = 0 because 0 is 0 units from zero.

Answer

|-9|=9, \quad |7|=7, \quad |0|=0
The magnitude (absolute value) measures distance from zero, ignoring direction. It is always non-negative. Negative inputs have their sign removed; positive and zero inputs are unchanged.

Example 2

medium
Which has greater magnitude: -15 or 12? Then determine which is greater as a signed number.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Evaluate |3 - 8|.

Example 2

medium
Solve |x| = 6. How many solutions are there?
← Back to Magnitude Formula Explained Practice Mode

Background Knowledge

These ideas may be useful before you work through the harder examples.

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