Standard form, units and significant figures

Overview

Recall questions on writing a quantity in standard form, the SI prefixes and converting between them, counting significant figures, the rules for rounding a calculated result, why an answer cannot be more precise than its least precise input, and worked conversions with real chemical quantities.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   Express a concentration of 0.0050 mol dm⁻³ in standard form, keeping the same number of significant figures.

   Model answer

   It is written 5.0 × 10⁻³ mol dm⁻³, with two significant figures preserved because the trailing zero in 0.0050 is significant.

2. 2

   A titration delivers 22.5 cm³ of solution. Express this volume in dm³.

   Model answer

   There are 1000 cm³ in 1 dm³, so the volume is 22.5 ÷ 1000 = 0.0225 dm³.

3. 3

   Convert a gas volume of 2.50 dm³ into cubic metres.

   Model answer

   One cubic metre contains 1000 dm³, so the volume is 2.50 × 10⁻³ m³.

4. 4

   An enthalpy change is quoted as −45.0 kJ mol⁻¹. Express it in J mol⁻¹ in standard form.

   Model answer

   Multiplying by 1000 gives −45 000 J mol⁻¹, which in standard form is −4.50 × 10⁴ J mol⁻¹.

5. 5

   Why must an entropy change be converted before it is combined with an enthalpy change in the free energy relationship?

   Model answer

   Entropy changes are tabulated in J mol⁻¹ K⁻¹ while enthalpy changes are quoted in kJ mol⁻¹, so one of them must be scaled by a factor of 1000 before they are subtracted, otherwise the answer is out by three orders of magnitude.

6. 6

   How many significant figures does the value 0.02040 mol dm⁻³ contain?

   Model answer

   It contains four, because the zeros before the 2 only fix the decimal point while the zero between the 2 and the 4 and the final zero are both significant.

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