This worksheet introduces logarithmic scales, teaching students to interpret and use pH, earthquake magnitude and decibel scales to compare quantities across an enormous range of values. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- A logarithmic scale compresses an enormous range of values (like [H⁺] concentration, or sound intensity) into small, manageable numbers using log₁₀.
- On a logarithmic scale, each whole number step represents a ten-times change in the underlying quantity — e.g. a magnitude 5 earthquake has 10 times the amplitude of a magnitude 4 earthquake.
- pH = −log₁₀[H⁺], where [H⁺] is the hydrogen ion concentration in mol/L — pH decreases as acidity (concentration) increases.
- Earthquake magnitude (Richter-style) M=log₁₀(A/A₀), where A is the amplitude of the earthquake's waves and A₀ is a reference amplitude.
- Sound level in decibels: L=10×log₁₀(I/I₀), where I is the sound intensity and I₀ is a reference intensity — the factor of 10 (not just log₁₀ alone) is specific to the decibel scale.
What your child will practise:
- Evaluating log₁₀ of a given number, including powers of 10.
- Converting between a logarithmic-scale value (pH, magnitude, decibels) and the underlying quantity, in both directions.
- Finding how many times larger one quantity is than another, given their logarithmic-scale values (using 10^(difference)).
- Finding the change in a logarithmic-scale reading that corresponds to a given multiplicative change in the underlying quantity.
- Expressing very small or very large underlying quantities in scientific notation.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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