Significant Figures

Transcript

Significant Figures Significant figures are the meaningful digits in a measured value. A measurement contains certain digits and a final estimated, or uncertain, digit. For example, in a measurement of 28.3 mL: Certain digits: 2 and 8 Uncertain digit: 3 Number of significant figures: 3 Significant figures = Certain digits + Final uncertain digit A more finely graduated instrument generally allows a more precise reading. 28 mL — 2 significant figures 28.3 mL — 3 significant figures 28.32 mL — 4 significant figures RULES 1. All non-zero digits are significant. 33.2 has 3 significant figures. 526 has 3 significant figures. 2. Zeros between non-zero digits are significant. 2051 has 4 significant figures. 105 has 3 significant figures. 1.008 has 4 significant figures. 3. Leading zeros are not significant. 0.54 has 2 significant figures. 0.0032 has 2 significant figures. Leading zeros locate the decimal point. 4. Trailing zeros after a decimal point are significant. 92.00 has 4 significant figures. 2.500 has 4 significant figures. 10.0 has 3 significant figures. 92.00 and 92 express different levels of precision. The additional zeros in 92.00 carry measurement information. 5. Trailing zeros in a whole number require care. A written decimal point can indicate that trailing zeros are significant. 540. has 3 significant figures. 300. has 3 significant figures. Without a decimal point or other information, trailing zeros may be ambiguous. Scientific notation makes the intended precision clear. 7 × 10³ — 1 significant figure 7.0 × 10³ — 2 significant figures 7.00 × 10³ — 3 significant figures 7.000 × 10³ — 4 significant figures 6. Exact numbers have unlimited significant figures. Counted quantities and exact definitions do not limit significant figures. Examples: 12 apples counted exactly. 1 m = 100 cm exactly. WORKED EXAMPLES 7.4 — 2 significant figures 526 — 3 significant figures 0.0032 — 2 significant figures 0.070 — 2 significant figures 105 — 3 significant figures 1.008 — 4 significant figures 2.500 — 4 significant figures 10.0 — 3 significant figures 0.04050 — 4 significant figures 0.0007090 — 4 significant figures 5.0600 — 5 significant figures 300. — 3 significant figures 7000 — ambiguous without further information 7.000 × 10³ — 4 significant figures 6.02 × 10²³ — 3 significant figures 12 apples counted exactly — unlimited significant figures The exponent in scientific notation does not affect the number of significant figures.