Sig. Figs. 3

Significant Figures 3.0

🧪 INSTRUCTIONS:

1) Take notes on Sig. Figs. Quick Examples below
2) Then Complete the Significant Figures 3 assignment (below)
3) Screenshot your name + score to the Google Classroom when finish

Significant Figures (Multiplication and Division)

Notebook Rule

Multiply/Divide → round by total significant figures.
Your final answer must have the same number of significant figures as the value with the fewest significant figures.

Find the sig figs in each value.
Do the multiplication or division on a calculator.
Identify the smallest sig-fig count among the inputs.
Round the final answer to that many sig figs.

Tips: Leading zeros never count (0.00450 has 3 sig figs). Exact counts and defined conversions (like 12 eggs, 1000 mL = 1 L) have unlimited sig figs and do not limit rounding.

Quick Examples

1) Area = 2.4 cm × 3.15 cm

Raw product: 2.4 × 3.15 = 7.56 cm²

Sig figs: 2.4 = 2 sf, 3.15 = 3 sf → fewest = 2.

Round 7.56 to 2 sig figs → 7.6 cm²

2) Density = 15.72 g ÷ 6.0 mL

Raw quotient: 15.72 ÷ 6.0 = 2.62 g/mL

Sig figs: 15.72 = 4 sf, 6.0 = 2 sf → fewest = 2.

Round 2.62 to 2 sig figs → 2.6 g/mL

3) 0.00450 m × 2.1 m

Raw product: 0.00450 × 2.1 = 0.00945 m²

Sig figs: 0.00450 = 3 sf, 2.1 = 2 sf → fewest = 2.

Round 0.00945 to 2 sig figs → 9.5 × 10⁻³ m² (or 0.0095 m²)

4) Speed = 150.0 m ÷ 12 s

Raw quotient: 150.0 ÷ 12 = 12.5 m/s

Sig figs: 150.0 = 4 sf, 12 = 2 sf → fewest = 2.

Round 12.5 to 2 sig figs → 13 m/s

5) Average mass = total mass ÷ 4 samples

Suppose total mass = 18.36 g; 18.36 ÷ 4 = 4.59 g

18.36 = 4 sf. The number 4 is an exact count (4 items) → unlimited sf (does not limit).

Round to the sig figs of the measured value (4 sf) → 4.590 g

Remember: Multiply/Divide → match the fewest sig figs. For add/subtract, you match the fewest decimal places instead (different rule).

Significant Figures 3.0

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