Significant Figures A K A Sig Figs Measuring
- Slides: 12
Significant Figures A. K. A Sig Figs Measuring with Precision
Sig Figs • #s that result from directly measuring an object. • Tells you where to round when no other directions are given. • Shows the precision of the measurement.
Rule 1: All nonzero digits are significant (they were measured) Samples Sig Figs & precision • a. 234 m • a. 3 sig figs • b. 1678 cm • b. 4 sig figs • c. 0. 23 g • c. 2 sig figs
Rule 2: All 0 s btwn nonzero digits are significant Translation: In btwn 0 s are significant Samples • a. 202 mm Sig Figs & precision • a. 3 sig figs • b. 1003 cm • b. 4 sig figs • c. 0. 200105 m • c. 6 sig figs
Rule 3: Zeros to the right of a nonzero digit but to the left of an understood decimal are NOT significant unless otherwise indicated. (WHAT? !? !) Translation: 0 s at the end of a whole number are NOT (with a or a. ) • significant unless marked • • • a. 200 cm b. 109, 000 m c. 1, 000 mm d. 200 cm • • a. b. c. d. 1 sig fig 3 sig figs (a bar over a zero indicates the last measured zero) • e. 200 cm • e. 2 sig figs
Rule 4: All zeros to the right of a decimal point but to the left of a nonzero digit are NOT significant. Translation: 0 s in front of a # < 1 are NOT significant Samples • a. 0. 0032 m Sig Figs & precision • a. 2 sig figs • b. 0. 01294 g • b. 4 sig figs • c. 0. 00000002 L • c. 1 sig fig
Rule 5: All 0 s to the right of a decimal point & following a nonzero digit are significant Translation: 0 s at the end of a decimal # are significant Samples • a. 20. 00 g Sig Figs & precision • a. 4 sig figs • b. 0. 07080 mm • b. 4 sig figs • c. 1. 0400 cm • c. 5 sig figs
When converting measurements • Rule: The converted measurement must have exactly the same precision as the original measurement. • Ex. When converting 6. 0 mg to g is the conversion. 006 g or. 0060 g? – 6. 0 g has 2 sig figs so the conversion must have 2 sig figs. Which conversion has 2 sig figs? – Answer: . 0060 g
How to use SF rules when adding/subtracting • Rule: Your answer must have the same amount of #s after the decimal as the number with the LEAST #s after the decimal in the original #s
How to use SF rules when multiplying/dividing • Rule: Your answer must have the same amount of sig. figs. as the LEAST # of sig. figs. in the original #s
Problems 1. 37. 76 + 3. 907 + 226. 4 = ? 2. 319. 15 - 32. 614 = ? 3. 104. 630 + 27. 08362 + 0. 61 = ? 4. 125 - 0. 23 + 4. 109 = ? 5. 2. 02 × 2. 5 = ?
Problems Cont. 6. 600. 0 / 5. 2302 = ? 7. 0. 0032 × 273 = ? 8. (5. 5)3 = ? 9. 0. 556 × (40 - 32. 5) = ? 10. 45 × 3. 00 = ? 11. What is the average of 0. 1707, 0. 1713, 0. 1720, 0. 1704, and 0. 1715?
