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Linear Versus Logarithmic Scale

Run the Linear Versus Logarithmic Scale MicroSim Fullscreen

About This MicroSim

You cannot argue someone into believing that a logarithmic scale is necessary. They have to see the linear version fail.

This chart plots relative ground motion for eight earthquakes from magnitude 2.0 to magnitude 9.1. Because each whole step of magnitude is a factor of ten in ground motion, the magnitude 9.1 event shakes the ground roughly 12.6 million times as far as the magnitude 2.0 event.

On the linear axis, seven of the eight bars are visually indistinguishable from zero. They are not zero. They are earthquakes that knock down buildings.

On the logarithmic axis, all eight become readable, and the even spacing between them exposes the factor-of-ten structure that the magnitude scale is built from.

The dataset is identical between the two views. Only the axis type changes, so there is nothing else the difference could be blamed on.

How to Use

  • Press Linear axis and Logarithmic axis to swap the y-axis scale type.
  • Hover any bar for the magnitude, the relative ground motion in scientific notation, and a plain-language description of what that shaking feels like.
  • Click any bar to pin a comparison with the magnitude 2.0 baseline, written both as a plain number and in scientific notation.
  • Read the caption above the plot. It changes with the axis.

Iframe Embed Code

You can add this MicroSim to any web page by adding this to your HTML:

<iframe src="https://iowerx.github.io/pi-env-monitor/sims/linear-versus-log-scale/main.html"
        height="504px"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan

Grade Level

6-12

Duration

15-20 minutes

Bloom's Taxonomy Level

Analyze (L4)

Prerequisites

  • Reading a bar chart
  • Knowing that 10^4 means 10000

Activities

  1. Prediction (3 min): Before touching anything, predict how tall the magnitude 7.0 bar will look next to the magnitude 9.1 bar. Then look at the linear view.
  2. Exploration (5 min): Click each bar in turn on the linear view and read the comparison. Note how large the numbers are for bars that look like nothing.
  3. Analysis (6 min): Switch to the logarithmic axis. Measure with your finger: is the gap from M3 to M4 the same height as the gap from M7 to M8? Explain what that equal spacing means.

Assessment

  • States why the linear view is misleading without calling it wrong.
  • Explains equal spacing on a log axis as equal ratios, not equal differences.
  • Names a second quantity from this book that would need a log axis.

References

  1. USGS: Earthquake magnitude, energy release, and shaking intensity - the factor-of-ten relationship used for the amplitudes here.
  2. USGS: Moment magnitude, Richter scale - what are the different magnitude scales?
  3. Wikipedia: Moment magnitude scale
  4. Wikipedia: Logarithmic scale