Unit 2Scientific Measurement

And Problem Solving in Chemistry

Precision and AccuracySignificant Figures

% errorMeasurement

Density

Accuracy vs PrecisionAccuracy: All the data representsthe true measurement.When a measurement is accurateIt is very close to the accepted value.

Generally, you want to be within5% or less of the accepted value.

Accuracy vs PrecisionPrecision: All the data is very Similar to the average value.The data is very reproducible.

It is not necessarily accurate. The measuring device could be consistent but not accurate.

The measurements will have been taken under the same conditions.

To be both Accurate and Precise

The data must be consistent AND near theAccepted value.

Precise, Accurate, or both?

 Trial 1Arrow # 1 = 0.4 cmArrow #2 = 0.6 cmArrow #3 = 1.0 cmArrow #4 = 1.2 cm

Water level

Trial 1Rf1 = 0.4/1.2 = 0.3Rf2 = 0.6/1.2 = 0.5Rf3 = 1.0/1.2 =0.83

Trial 2Arrow # 1 = 0.3 cmArrow #2 = 0.5 cmArrow #3 = 0.9 cmArrow #4 = 1.1 cm

Trial 2Rf1 = 0.3/1.1 = 0.3Rf2 = 0.5/1.1 = 0.5Rf3 = 0.9/1.1 =0.8

These are both accurate and precise

Rf = .3 Rf = .5 Rf = .8

Precise, Accurate, or both?

 Trial 1Arrow # 1 = 0.6 cmArrow #2 = 0.8 cmArrow #3 = 1.1 cmArrow #4 = 1.2 cm

Water level

Trial 1Rf1 = 0.6/1.2 = 0.5Rf2 = 0.8/1.2 = 0.7Rf3 = 1.1/1.2 =0.92

Trial 2Arrow # 1 = 0.6cmArrow #2 = 0.8cmArrow #3 = 0.9 cmArrow #4 = 1.1 cm

Trial 2Rf1 = 0.6/1.1 = 0.5Rf2 = 0.8/1.1 = 0.7Rf3 = 1.0/1.1 =0.91

These are onlyprecise

Rf = .3 Rf = .8Rf = .5

% error – instead of guessing if data is precise or accurate, you can use statistics.Error = Accepted Value – experimental value.In order to use % error, you must be using a

substance for which there IS an accepted value. In one of our next chemistry lab, we will be using Appendix A1 to compare our values of density of elements to your experimental values.

ErrorAccepted Value – experimental

value.

Accepted Value

% error = x 100%

Accepted Value

Significant Figures1. Non Zero Numbers are

significant2. Zeros in between significant

digits are significant3. Place-holder zeros are NOT

significant. All other zeros are.

4. Scientific notation is used if a zero which SHOULD be a place-holder is actually a measured value.

1.234 = 4 sig figs1.01 = 3 sig figs10004 = 5 sig figs0.0001 = 1 sig fig10000 = 1 sig fig101000 = 3 sig

figs1.0 x 108 = 2 sig

figs

Scientific Notation1101001 00010 000100 0001 000 00010 000

000

1 x 100

1 x 101

1 x 102

1 x 103

1 x 104

1 x 105

1 x 106

1 x 107

0.10.010.0010.000 10.000 010.000 0010.000 000

10.000 000

01

1 x 10-1

1 x 10-2

1 x 10-3

1 x 10-4

1 x 10-5

1 x 10-6

1 x 10-7

1 x 10-8

Test Yourself…1. 9009.002. 30003. 0.0004044. 5645. 0.01006. 0.0004347. 45400008. 9.400 x 1010

9. 1.90 x 10-4

1. 9009.00 = 6 sig figs2. 3000 = 1 sig fig3. 0.000404= 3 sig figs4. 564 = 3 sig figs5. 0.0100 = 3 sig figs6. 0.000434 = 3 sig figs7. 4540000 = 3 sig figs8. 9.400 x 1010 = 4 sig figs9. 1.90 x 10-4 = 3 sig figs

Test Yourself….Round each number to two sig figs.

1. 9009.002. 30003. 0.0004044. 5645. 0.01006. 0.0004347. 45400008. 9.400 x 1010

9. 1.90 x 10-4

1. 9.0 x 103

2. 3.0 x 103

3. 4.0 x 10-4

4. 5.6 x 102

5. 1.0 x 10-2

6. 4.3 x 10-4

7. 4.5 x 106

8. 9.4 x 1010

9. 1.9 x 10-4

Find the density of a metalFind the mass using a balanceFind the volume either using rulers or

using measurement by difference.Density = mass/volumeLook up the accepted value for density.

% error = 100% x Accepted – Experimental

Accepted