AC9M10M02Year 10MeasurementPractised on site

AC9M10M02 — Year 10 Measurement

Official Curriculum Content Description:

interpret and use logarithmic scales  in applied contexts involving small and large quantities and change

Worked Examples (1)

Example 1Logarithmic Scales & Order of Magnitude

A laboratory sample has a

\text{pH}

2

, compared to a second sample with a

\text{pH}

4

. By what factor is the hydrogen ion concentration greater in the first sample than in the second sample? (Each decrease of

1

on the

\text{pH}

scale represents a

10

-fold increase in hydrogen ion concentration.)

Common mistake: Using the difference in pH (2) or multiplying by 10 (20) instead of computing

10^{2}

Correct Answer:

100

Worked Solution:

The difference in

\text{pH}

4 - 2 = 2

. Each decrease of

1

unit multiplies the hydrogen ion concentration by

10

, so the concentration ratio is

10^{2} = 100

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