2.3 2.3 Using Scientific Using Scientific MeasurementsMeasurements

Accuracy vs. PrecisionAccuracy vs. Precision

AccuracyAccuracy- closeness of measurement to - closeness of measurement to correct or accepted valuecorrect or accepted value

PrecisionPrecision- closeness of a set of - closeness of a set of measurementsmeasurements

Accuracy vs. PrecisionAccuracy vs. Precision

Significant FiguresSignificant Figures

All certain digits plus All certain digits plus one estimated digitone estimated digit

Determining Number of Sig FigsDetermining Number of Sig Figs

All non-zero numbers are sig figsAll non-zero numbers are sig figs Zeros depend on location in number:Zeros depend on location in number:

LEADING zeros LEADING zeros nevernever count count

EMBEDDED zeros EMBEDDED zeros alwaysalways count count

TRAILING zeros TRAILING zeros onlyonly count if count if

there is a decimal point.there is a decimal point.

Location of Zeros Location of Zeros

1.1. EMBEDDED: EMBEDDED: between non-zero numbersbetween non-zero numbers All are sig figsAll are sig figs

2.2. LEADING: LEADING: at front of all non-zero numbersat front of all non-zero numbers None are sig figsNone are sig figs

3.3. TRAILING:TRAILING: at the end of non-zero numbers at the end of non-zero numbers If there is a decimal, all are sig figsIf there is a decimal, all are sig figs If there is not, none are sig figsIf there is not, none are sig figs

PracticePractice

101.02101.02 EMBEDDEDEMBEDDED 55

20.020.0 TRAILING w/TRAILING w/ 33

0.0053020.005302 LEADINGLEADING 44

1700017000 TRAILING w/oTRAILING w/o 22

4320.4320. TRAILING w/TRAILING w/ 44

RoundingRounding

Need to use rounding to write a calculation Need to use rounding to write a calculation correctlycorrectly

Calculator gives you lots of insignificant Calculator gives you lots of insignificant figures and you must round to the right figures and you must round to the right placeplace

When rounding, look at the digit after the When rounding, look at the digit after the one you can keepone you can keep Greater than or equal to 5, round upGreater than or equal to 5, round up Less than 5, keep the sameLess than 5, keep the same

ExamplesExamples

Make the following have 3 sig figs:Make the following have 3 sig figs: 761.50 761.50 762762 14.334 14.334 14.314.3 10.4410.44 10.410.4 1078910789 1080010800 8024.508024.50 80208020 203.514203.514 204204

Using Sig Figs in CalculationsUsing Sig Figs in Calculations

Adding/Subtracting:Adding/Subtracting: end with the least number of decimal placesend with the least number of decimal places

Using Sig Figs in CalculationsUsing Sig Figs in Calculations

Adding/Subtracting:Adding/Subtracting: end with the least number of decimal placesend with the least number of decimal places

Using Sig Figs in CalculationsUsing Sig Figs in Calculations

Multiplying/Dividing:Multiplying/Dividing: end with the least number of sig figsend with the least number of sig figs

Using Sig Figs in CalculationsUsing Sig Figs in Calculations Multiplying/Dividing:Multiplying/Dividing:

end with the least number of sig figsend with the least number of sig figs