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## SIGNIFICANT DIGITS

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**SIGNIFICANT DIGITS**& Significant Zero Rules**SIGNIFICANT DIGITS:**Represent numbers that are actually measured with some type of a measurement device.**SIGNIFICANT DIGITS**• Sig Digs will include all certain digits plus ONEestimated digit. 5.632 g certain digits estimated digit**SIGNIFICANT DIGITS**• certain digits: have calibrated markings on the instruments • estimated digits: between the 2 markings (if right on a marking, your est. is 0)**Uncertainty of last digit:**…is assumed to be + or -1 unless other wise stated.**ROUNDING**1. If the decimal is greater than 0.5 round up 2. If the decimal is less than 0.5 round down 3. If the decimal is exactly 0.5 (ex: 20.5) round up**Reading an Instrument**The more calibrated marks on the instruments, the more sig digs are in your measurement--the more accurate your measurement!**SIGNIFICANT DIGITS EXAMPLES**1 2 What would the measurement be?**SIGNIFICANT DIGITS EXAMPLES**4 5 What would the measurement be?**SIGNIFICANT DIGITS EXAMPLES**How long is the green line?**SIGNIFICANT DIGITS EXAMPLES**What would the measurement be?**SIGNIFICANT DIGITS EXAMPLES**What would the measurement be?**Significant Figures – Rules**1. Every nonzero digit in a reported measurement is assumed to be significant. Example: 24.7 m, 0.743 m, and 714 m all have ___ sig figs.**Significant Figures – Rules**2. Captive zerosalways count as significant figures. Example: 7003 m, 40.79 m, and 1.503 m all have ___ sig figs.**Significant Figures – Rules**3. Leading zeros do NOT count as significant figures. Example: 0.0071 m, 0.000099 m, and 0.42 m all have ___ sig figs. *Scientific Notation…we’ll talk about this later**Significant Figures – Rules**4. Trailing zeros are significant only if the number contains a decimal point. Example: 43.00 m, 1.010 m, and 9.000 m all have ___ sig figs.**Significant Figures – Rules**5. Trailing zeros are NOT significant when there is not a decimal point Example: 200 m, 7000 m, and 10,000 m all have ___ sig fig.**WHICH ZEROES ARE SIGNIFICANT?**6.002 10.50 269.00 0.009 0.50 6.770 150**Unlimited Sig Figs!**• Counting If you count 23 people in the room, there are exactly 23 people and the number has an infinite number of “understood” zeros behind it. • Exactly Defined Quantities Example: there are EXACTLY 60 minutes in 1 hour.**Sig Fig Practice**How many significant figures in each of the following? 1.0070 m 5 sig figs 17.10 kg 4 sig figs 100,890 L 5 sig figs 3.29 x 103 s 3 sig figs 0.0054 cm 2 sig figs 3,200,000 2 sig figs