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Significant Figures. Why do we need to know significant figures?. We as scientists need to measure things as we perform experiments. Instruments have different degrees of precision We measure to the last known calibration, and estimate the unknown. Significant = replaceable.
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Why do we need to know significant figures? • We as scientists need to measure things as we perform experiments. • Instruments have different degrees of precision • We measure to the last known calibration, and estimate the unknown.
Significant = replaceable • A number is significant because it can be replaced by another number in a measurement
Significant Figures – The Rules • 1. Nonzero numbers 1 – 9 are always significant. • Examples: • 1 meter 1 sig fig • 92liters 2 sig figs • 34578grams 5 sig figs
Significant Figures – The Rules • 2. Imbedded zeros (zeros between nonzero numbers) are always significant. • Examples: • 202cm 3 sig figs • 10509mL5 sig figs • 2039kg 4 sig figs • 90009g 5 sig figs
Significant Figures – The Rules • 3. Leading zeros are never significant. • 4. Trailing zeros after a nonzero number after the decimal are significant. • Examples: • 0.00000540 g 3 sig figs • 0.3700 mm 4 sig figs • 0.00101 L 3 sig figs
Significant Figures – The Rules • 5. Trailing zeros before the decimal are significant only if the decimal point is specified. • Examples: • 100. dg 3 sig figs • 100 dg 1 sig fig • 8900 km 2 sig figs • 8900. km 4 sig figs
Exact Numbers • An exact number is a number that cannot be changed. (Cannot be halved or split up) • Ex. 2 atoms, 1 proton, a hundred dollar bill • We include most conversion factors as exact numbers • Ex. 1m = 100 cm • When you work with exact numbers, you consider them to have infinite sig figs. (You don’t have to worry about them!)
RECAP #1 Leading Zeros Imbedded Zero 0.00770800 Nonzero numbersTrailing Zeros after the decimal
RECAP #2 Leading Zeros Imbedded Zero (none) 22060 Nonzero numbersTrailing zero with no decimal
56 meters • 2 sig figs • Rule 1
20 grams 1 sig fig Rule 1, 5
303.0 mL 4 sig figs Rule 1, 2, 4
200 dollars 1 sig fig Rule 1, 5
207 donkeys 3 sig figs Rule 1,2
0.7900 grams 4 sig figs Rule 1,3,4
0.0096070 m 5 sig figs Rule 1,2,3,4
102000 km 3 sig figs Rule 1,2,5
1.10 x 102 hm 3 sig figs Rule 1, 4
2.2 x 1034 atoms 2 sig figs Rule 1
Rounding Numbers • If you have to round and the number you are looking to round is less than 5, don’t round. • Example: 214 round to 2 s.f. Answer = 210
Rounding Numbers • If you have to round and the number you are looking to round is 5 or greater, round up. • Example: 215 round to 2 s.f. Answer = 220