SIGNIFICANT DIGITS

& Significant Zero Rules

SIGNIFICANT DIGITS:SIGNIFICANT DIGITS:

Represent numbers that are actually measured with some type of a measurement device.

SIGNIFICANT DIGITSSIGNIFICANT DIGITS•Sig Digs will include all certain digits plus ONEONE estimated digit.

5.632 g

certain digits

estimated digit

certain digits: have calibrated markings on the instruments

estimated digits: between the 2 markings (if right on a marking, your est. is 0)

SIGNIFICANT DIGITSSIGNIFICANT DIGITS

Uncertainty of last digit:Uncertainty of last digit:

…is assumed to be + or -1 unless other wise stated.

ROUNDINGROUNDING

1. If the decimal is greater than 0.5 round up2. If the decimal is less than 0.5 round down3. If the decimal is exactly 0.5 (ex: 20.5) round up

Reading an InstrumentReading an Instrument

The more calibrated marks on the instruments, the more sig digs are in your measurement--the more accurate your measurement!

SIGNIFICANT DIGITS SIGNIFICANT DIGITS EXAMPLESEXAMPLES

1 2

What would the measurement be?

SIGNIFICANT DIGITS SIGNIFICANT DIGITS EXAMPLESEXAMPLES

4 5

What would the measurement be?

SIGNIFICANT DIGITS SIGNIFICANT DIGITS EXAMPLESEXAMPLES

How long is the green line?

SIGNIFICANT DIGITS SIGNIFICANT DIGITS EXAMPLESEXAMPLES

What would the measurement be?

SIGNIFICANT DIGITS SIGNIFICANT DIGITS EXAMPLESEXAMPLES

What would the measurement be?

Significant Figures – RulesSignificant Figures – Rules

1. Every 1. Every nonzero digitnonzero digit in a reported in a reported measurement is assumed to be measurement is assumed to be significant.significant.

Example: Example:

24.7 m, 0.743 m, and 714 m 24.7 m, 0.743 m, and 714 m

all have ___ sig figs. all have ___ sig figs.

Significant Figures – RulesSignificant Figures – Rules

2. 2. Captive zerosCaptive zeros alwaysalways count as count as significant figures.significant figures.

Example: Example:

7003 m, 40.79 m, and 1.503 m 7003 m, 40.79 m, and 1.503 m

all have ___ sig figs. all have ___ sig figs.

Significant Figures – RulesSignificant Figures – Rules

3. 3. Leading zerosLeading zeros do NOT count as do NOT count as significant figures.significant figures.

Example: Example:

0.0071 m, 0.000099 m, and 0.42 m 0.0071 m, 0.000099 m, and 0.42 m all have ___ sig figs. all have ___ sig figs.

*Scientific Notation…we’ll talk about this later*Scientific Notation…we’ll talk about this later

Significant Figures – RulesSignificant Figures – Rules

4. 4. Trailing zerosTrailing zeros are significant are significant only ifonly if the number contains a decimal the number contains a decimal point.point.

Example: Example: 43.00 m, 1.010 m, and 9.000 m 43.00 m, 1.010 m, and 9.000 m

all have ___ sig figs. all have ___ sig figs.

Significant Figures – RulesSignificant Figures – Rules

5. 5. Trailing zerosTrailing zeros are NOT are NOT significant when there is not a significant when there is not a decimal pointdecimal point

Example: Example: 200 m, 7000 m, and 10,000 m 200 m, 7000 m, and 10,000 m

all have ___ sig fig. all have ___ sig fig.

WHICH ZEROES ARE WHICH ZEROES ARE SIGNIFICANT?SIGNIFICANT?6.0026.00210.5010.50269.00269.000.0090.0090.500.506.7706.770150150

Unlimited Sig Figs!Unlimited Sig Figs!

1.1. CountingCountingIf you count 23 people in the room,If you count 23 people in the room,there are exactly 23 people and thethere are exactly 23 people and thenumber has an infinite number ofnumber has an infinite number of““understood” zeros behind it.understood” zeros behind it.

2.2. Exactly Defined QuantitiesExactly Defined QuantitiesExample: there are EXACTLY 60 minutes in 1 Example: there are EXACTLY 60 minutes in 1

hour. hour.

Sig Fig PracticeSig Fig PracticeHow 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