Chapter 2 “Scientific Measurement” Standards for Measurement Accuracy vs. Precision Significant Figures.

Chapter 2“Scientific

Measurement”

• Standards for Measurement• Accuracy vs. Precision• Significant Figures

International System of Units

1. Measurements depend upon units that serve as reference standards

2. The standards of measurement used in science are those of the Metric System

The Fundamental SI Units (Le Système International, SI)

3. All other measurements are derived (or calculated) from the measurements in the SI System.

4. The following are some derived units used in science.

Volume Any cubic unit of lengthArea Any square unit of lengthDensity Any mass unit per volume Velocity Any unit of length per timeConcentration Any unit of mass per volume

All derived units are based on using a formula.Example : volume = (L)(W)(H)

Accuracy vs. Precision 5. It is necessary to make good,

reliable measurements in the lab

6. Accuracy – how close a measurement is to the true value

7. Precision – how close the measurements are to each other (repeatability)

a. Precision also reflects the number of decimal places in a measurement.

For example:

2.500 grams is more precise than 2.5 grams.

Precision and Accuracy

Neither accurate

nor precise

Precise, but not

accurate

Precise AND

accurate

Example:Technician A and B measured the density of a substance several times. The actual density is 2.70 g/ml. Which technician was more precise and which was more accurate and why?

Tech A Tech B2.000 g/ml 2.5 g/ml1.999 g/ml 2.9 g/ml2.001 g/ml 2.7 g/ml

Accuracy, Precision, and Error

8. Accepted value = the correct value based on reliable references (you can look this one up)

9. Experimental value = the value measured in the lab (you came up with this in lab)

Accuracy, Precision, and Error

10. Error = accepted value – exp. value Can be positive or negative

11. Percent error = the absolute value of the error divided by the accepted value, then multiplied by 100%

| accepted value – exp. value |

accepted value x 100%% error =

Significant Figures in Measurements

12. Significant figures in a measurement include all of the digits that are known, plus one more digit that is estimated.

13. Measurements must be reported to the correct number of significant figures.

Figure 3.5 Significant Figures:

Which measurement is the best?

What is the measured value?

What is the measured value?

What is the measured value?

Reading for graduated cylinders

Read at the bottom of the meniscus.Include one more digit than the smallest division.Reading = 35.0 mls not 35 mls

Rules for Counting Significant Figures

1. Non-zerosNon-zeros always count as always count as significant figures:significant figures:

34563456 hashas

44 significant figuressignificant figures

Rules for Counting Significant Figures

2. 2. LeadingLeading zeroes do not count zeroes do not count as significant figures:as significant figures:

0.04860.0486 has has

33 significant figures significant figures

Rules for Counting Significant Figures

3. 3. CaptiveCaptive zeroes always count zeroes always count as significant figures:as significant figures:

16.0716.07 hashas

44 significant figures significant figures

Rules for Counting Significant Figures

4. 4. TrailingTrailing zeros (or zeros after a non- zeros (or zeros after a non-zero digit)zero digit) are significant only if the are significant only if the number contains a written number contains a written decimaldecimal point: point:

9.3009.300 has has 44 significant figures significant figures

100100 has has 11 significant figure significant figure

100100..00 has has 44 significant figures significant figures

Sig Fig Practice #1How many significant figures in 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 mL 2 sig figs

These all come from some measurements