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Lesson · Grade 11 · Chemistry

Significant Figures: How Precise Is Your Answer?

  • Grade 11
  • Chemistry
  • 1 min 53 s
  • British Columbia
  • BC11-SC-22

A paper strip measured on a millimetre ruler reads 4.56 cm: the 4 and the 5 are certain and the 6 is estimated by eye, which explains what significant figures are, and four rules for counting them follow (non-zero digits, zeros between them, leading zeros, trailing zeros after a decimal point). The strip's area, 4.56 cm × 1.4 cm, shows that the calculator's 6.384 must be cut to the fewest significant figures (6.4 cm²), and 12.11 g + 0.3 g shows that adding keeps the fewest decimal places (12.4 g), ending on the recap that an answer is never more precise than its measurements.

Concept: Significant figures in measurements and calculations

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In one sentence

The question this lesson answers

A calculator gives you an answer like 6.384. Should you keep every digit?

Start with a measurement. This ruler has millimetre marks.

Transcript

What the lesson says

A calculator gives you an answer like 6.384. Should you keep every digit?

Start with a measurement. This ruler has millimetre marks.

Zoom in. The end is past 4.5 centimetres, but not at 4.6.

So we estimate one more digit by eye: 4.56 centimetres.

The 4 and the 5 are certain. The 6 is an estimate.

These are the significant figures, or sig figs. 4.56 has three.

Non-zero digits count, and so do zeros between them: 2.05 has three.

Leading zeros never count. They only place the decimal point: 0.045 has two.

Trailing zeros count after a decimal point: 3.40 has three.

Back to the strip: it is 1.4 centimetres wide. A calculator gives its area as 6.384 square centimetres.

But a long calculator answer is no more precise than the measurements.

For multiplying or dividing, keep the fewest sig figs: 4.56 has three, 1.4 has two.

So the area is 6.4 square centimetres.

Now add 12.11 grams and 0.3 grams. The calculator says 12.41.

For adding or subtracting, keep the fewest decimal places: one here, so 12.4 grams.

An answer is never more precise than the measurements it comes from.

Curriculum

Where this fits

British Columbia, Grade 11

Chemistry 11, The mole and stoichiometry: dimensional analysisBC11-SC-22

Previous: The factor-label method: let the units guide youNext: Grams to Moles to Particles

The outcomes and strands follow the British Columbia curriculum.

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