Scientific Measurement

Types of measurementQuantitative- use numbers to describe

Qualitative- use description without numbers

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Scientists prefer QUANTITATIVE as there is no room for bias!

Remember…

Numbers without units are meaningless.

NO NAKED NUMBERS!!!

How good are measurements?Accuracy- how close the measurement is to the true value

Precision- how well can the measurement be reproduced

Let’s use a golf anaolgy

Accurate? No

Precise? Yes

Accurate? Yes

Precise? Yes

Precise? No

Accurate? No

Accurate? Yes

Precise? We can’t say!

Significant figures (sig figs)How many numbers in a measurement

means somethingWhen we measure something, we can

(and do) always estimate between the smallest marks.

21 3 4 5

Significant figures (sig figs)More marks = More precision

Scientists always understand that the last

number measured is actually an estimate

21 3 4 5

Go to your lab stationNote the smallest scale marks for each, and to what place you should estimate:100 mL Grad Cyl50 mL Grad Cyl25 mL Grad Cyl10 mL Grad Cyl50 mL Buret100 mL BuretElectronic balance

1mL so, est.→ 0.1 mL

1mL so, est.→ 0.1 mL

0.2 mL so, est.→ 0.1 mL

0.1mL so, est.→ 0.01 mL

0.1mL so, est.→ 0.01 mL

0.2 mL so, est.→ 0.1 mL

0.01 g

Sig Figs (sig digs)Since science tools aren’t precise to infinite digits,

we say only certain numbers are

“significant” to us.

Atlantic/Pacific RuleNumber AtlanticPacific

• If decimal is “Present” start counting from the Pacific Side at the first “non-zero” digit and continue counting until the number ends.

• If the decimal is “Absent” start counting from the Atlantic side at the first “non-zero” digit and continue counting until the number ends.

How many sig figs in these measurements?

#1: 458 g3#2: 4850 g3#3: 0.0485 g3#4: 40.0040850 g9

Which measurement has 3 sig figs?A.2.013B.4200C.74.0D.830

Round the following numbers to three sig figs.

#1: 47.38947.4

#2: 3075.2163080

#3: 0.187520.188

Round 5458.4999 to four sig figs.A.5459B.5500.C.5458D.5500.00

What about this measurement?

How many significant figures should you have?

How do you write 30 with two sig figs?

30.

2010 30 40 50

Adding and Subtracting with sig figs

Your answer when you add or subtract can not be more “significant” than your worst estimate.

Find the answer, then round to the least significant place of any measurement in the problem

For example

27.93 6.4+ = 34.33

Tenths place(least preciseMeasurement)

Also tenths place

Find the answer first, then round to the least significant place of any measurement in the problem.

Practice#1: 4.8 + 6.876511.6765 = 11.7#2: 0.0045 + 2.1132.1175 = 2.118#3: 6.7 - .5426.158 = 6.2

14.442 – 2.00 = ?A.12.44B.12.442C.12.440D.12.50

Multiplication and DivisionRule is different from addition and

subtractionAnswer has the same number of sig figs

as the least significant number in the problem

3.6 x 653 = 2350.82 sig figs 3 sig figs Can ONLY have 2 sig figs

= 2400

Remember, the rules are the same for division.

Multiplication and Division#1) 4.5 / 6.245 = 0.720576461169

= 0.72#2) 4.5 x 6.245 = 28.1025= 28#3) 3.876 / 1983 = 0.001954614221

= 0.001955