Magnitude Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Which has greater magnitude: −15-15 or 1212? Then determine which is greater as a signed number.

Solution

  1. 1
    Magnitude of −15-15: ∣−15∣=15|-15| = 15. Magnitude of 1212: ∣12∣=12|12| = 12.
  2. 2
    Since 15>1215 > 12,   ∣−15∣\;|-15| has greater magnitude.
  3. 3
    As signed numbers: −15<12-15 < 12 because −15-15 is to the left of 1212 on the number line.

Answer

∣−15∣>∣12∣ (magnitude); but −15<12 (signed value)|-15| > |12| \text{ (magnitude); but } -15 < 12 \text{ (signed value)}
Magnitude and signed comparison give different answers. Magnitude asks 'how big?', ignoring sign. Signed comparison asks 'which is further right on the number line?'. These are different questions with different answers.

About Magnitude

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.

Learn more about Magnitude →

More Magnitude Examples

Example 1 easy

Find the magnitude (absolute value) of each: [formula], [formula], [formula].

Example 3 easy

Evaluate [formula].

Example 4 medium

Solve [formula]. How many solutions are there?

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