MEASUREMENT(A Quantitative Observation)

• MEASUREMENTS always have 2 things:

Number & Unit

• All measurements have error in them!

• A measurement consists of all known digits that can be known accurately PLUS one digit that is ESTIMATED.

• The estimated digit is always at the END of the number in a measurement.

MEASUREMENT& Degrees of Error

• The closer a measurement is to the true value, the more accurate the measurement.

• Accurate measurements are “more correct” and closer to the true value.

• Accuracy = Correctness.• How close a series of measurements are to one

another is called precision.• Precise measurements are close in value to one

another; repeated measures are precise. • Precision = Reproducibility.

Accuracy vs. Precision

• Another example: a 5 lb bag of potatoes is weighed by 3 people, 3 times each.

Person 1

4.9 lbs

4.8 lbs

4.85 lbs

Person 2

4.0 lbs

3.5 lbs

5 lbs

Person 3

4.0 lbs

4.1 lbs

4.2 lbs

Good Accuracy

Good Precision

Poor Accuracy

Poor Precision

Poor Accuracy

Good Precision

Determining Error• Accepted value is the correct value based

on reliable references.

• Reference: boiling point of water is 100.0°C

• Experimental value: temperature of boiling water measured to be 99.1°C

• ERROR = experimental – accepted value

• ERROR = (99.1°C – 100.0 °C) = –0.9 °C• (-) means your measurement was less

than the number of the true value. • (+) means your measurement is greater

than the true value.• PERCENT ERROR is an absolute value:

• %ERROR = (0.9/100) x 100 = 0.9%

100% accepted

errorerror

A way to express very large or very small numbers easily.

Example:

.0000000000000036333 seconds

= 3.6333 x 10-15 seconds

= 9.8765 x 1012 minutes

9876500000000 minutes

SCIENTIFIC NOTATION

Practice

(1) .000565 g 5.65 x 10-4 g

(2) 565000 s

5.65 x 105 s

(3) 43454 min

4.3454 x 104 min(4) .0010 L 1.0 x 10-3 L

Measurement Limitations

• ALL measurements have error in them!• A measurement consists of all known digits that

can be known accurately PLUS one digit that is estimated.

• The estimated digit is always at the end of the number in a measurement.

• All of the digits that are known in a measurement are significant figures.

• Fewer significant figures = more rounding in a measurement = more error.

What are the following lengths (in meters)?

(A)

(B)

(C)

ANSWERS

(A) 0.3 m (1 decimal place)

(B) 0.26 m (2 decimal places)

(C) 0.260 m (3 decimal places)

What is the density of a sample with a mass of 24.47 g and a volume of 13.2 mL? 

  A.  1.9 g/mL   B.  1.8537 g/mL   C.  1.854 g/mL   D.  1.85 g/mL

APPLYING SIG FIGS to MEASUREMENT:

HINT: Your FINAL answer cannot be more accurate than the least accurate measurement.

What is the density of a sample with a mass of 24.47 g and a volume of 13.2 mL? 

  A.  1.9 g/mL   B.  1.8537 g/mL   C.  1.854 g/mL   D.  1.85 g/mL

APPLYING SIG FIGS to MEASUREMENT:

Because 13.2 mL is accurate to only one decimal place, the answer can be no more accurate than one decimal place.

Easy Rules To Sig Figs

• ALL trailing zeros in a non-decimal are NOT significant (they act as placeholders only)

• ALL leading zeros in a decimal are NOT significant (they act as placeholders only)

• Sandwhiched zeros count (i.e. 101, 0.101)

• In a decimal, if the zero in question has a number 1 thru 9 before it anywhere in the number, it is significant! (i.e. 0.000000100000)

Putting It ALL Putting It ALL TogetherTogether

the speed of light = 299 792 458 m / s9 significant figures (sig figs)2.99 792 458 x 108 m/s8 sig figs = 2.99 792 46 x 108 m/s7 sig figs = 2.99 792 5 x 108 m/s6 sig figs = 2.99 792 x 108 m/s5 sig figs = 2.99 79 x 108 m/s4 sig figs = 2.99 8 x 108 m/s3 sig figs = 3.00 x 108 m/s2 sig figs = 3.0 x 108 m/s1 sig figs = 3 x 108 m/s

ROUNDING 123 456 789

• 123456790• 123456800• 123457000• 123460000• 123500000• 123000000• 120000000• 100000000

= 1.2345679 x 108

= 1.234568 x 108

= 1.23457 x 108 = 1.2346 x 108

= 1.235 x 108

= 1.23 x 108

= 1.2 x 108

= 1 x 108

Determine the Significant Figures• 1.0 blah

• 100000000.0 blah

• 100 blah

• 100. blah

• 0.10 blah

• 0.01 blah

• 0.010 blah

• 101 blah

Answers• 1.0 blah 2 sig figs

• 100000000.0 blah 10 sig figs

• 100 blah 1 sig fig

• 100. blah 3 sig figs

• 0.10 blah 2 sig figs

• 0.01 blah 1 sig fig

• 0.010 blah 2 sig figs

• 101 blah 3 sig figs

Answers in Scientific Notation• 1.0 x 100 blah 2 sig figs

• 1.000000000 x 108 blah 10 sig figs

• 1 x 102 blah 1 sig fig

• 1.00 x 102 blah 3 sig figs

• 1.0 x 10-1 blah 2 sig figs

• 1 x 10-2 blah 1 sig fig

• 1.0 x 10-2 blah 2 sig figs

• 1.01 x 102 blah 3 sig figs