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Analysis

Significant figures and mathematical processing

  • 3 things to know
  • Components 01, 02 and 03

Overview

Recall questions on significant figures in measurements and calculated results, decimal places for a mean, standard form and calculator entry, percentage change, scaling R = ρL/A, rearranging E = mc² and T = 2π√(L/g), order of magnitude calculations, and the symbols ∝, Δ, ≈, ≪ and ≫.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Numbers

To how many significant figures is a result quoted? Find the density of 24.0 g in 3.2 cm³, and why is 1500 ambiguous?

Key term

What is meant by the symbol ∝ between two quantities, and by Δ written before a quantity?

Key term

To how many significant figures should a calculated result be quoted?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    To how many significant figures should a calculated result be quoted?

    Model answer

    To the same number of significant figures as the least precise measurement it was calculated from.

  2. 2

    How many significant figures does the value 0.003 40 m contain?

    Model answer

    It contains three significant figures, because leading zeros only fix the decimal place while the trailing zero is a measured digit.

  3. 3

    What is the difference between recording a length as 2.5 cm and as 2.50 cm?

    Model answer

    The first claims the length is known to the nearest 0.1 cm and the second to the nearest 0.01 cm, so they state different resolutions.

  4. 4

    Express 0.045 678 9 m to three significant figures.

    Model answer

    It is 0.0457 m.

  5. 5

    A block of mass 24.0 g has a volume of 3.2 cm³. Calculate its density and quote it to an appropriate number of significant figures.

    Model answer

    The density is 24.0 ÷ 3.2 = 7.5 g cm⁻³, quoted to two significant figures because the volume is known to only two.

  6. 6

    To how many decimal places should the mean of a set of repeated readings be quoted?

    Model answer

    To the same number of decimal places as the individual readings, since averaging cannot improve the resolution of the instrument.

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