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Ch 3 Scientific Measurement. Measurements and Calculations in Chemistry. Accuracy refers to the closeness of measurements to the correct or accepted value of the quantity measured. Precision refers to the closeness of a set of measurements of the same quantity made in the same way. .

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slide3

Accuracy refers to the closeness of measurements to the correct or accepted value of the quantity measured.

  • Precision refers to the closeness of a set of measurements of the same quantity made in the same way.
slide4

Percent Error tells you how far away you are from the accepted value

Percent error = observed – accepted x 100

accepted value

*note: observed value is also the experimental value 

  • Example: Calculate the percent error of a measurement of .225 cm if the correct value is .229 cm.
  • Ans. 1.75%
slide5

Ex #2/ A student measures three trials of density of gold: 19.2 g/mL, 18.9 g/mL, and 19.0 g/mL. If gold’s actual density is 19.3 g/mL, what is the percent error?

Ans.  -1.55%

  • Error or uncertainty exists in any measurement.
  • Ex/ some balances can be read more precisely than others (more places after the decimal)
slide6

Significant Figures in a measurement consists of all the digits known with certainty plus one final digit which is uncertain or estimated.

rules of significant numbers and zeros
Rules of Significant Numbers and Zeros
  • 1. All non-zero numbers in a measured quantity are significant.
  • Ex: 2.34 m= 3 significant figures
  • 2. Zeros appearing between nonzero digits are significant.
  • Ex: 2.04 km = 3 SFs, 24.005 m= 5 SFs
slide8

3. Zeros appearing in front of nonzero digits are not significant.

  • Ex: 0.002345 m= 4 SFs
  • 4. Zeros at the end of a number and to the right of the decimal are significant.
  • Ex: 23.400 kg = 5 SFs, 0.0023400 kg = 5 SFs
slide9

5. Zeros at the end of a number and to the left of the decimal may or may not be significant. It depends on whether it was measured or if it is a placeholder.

NOTE: If there is a decimal after the zeros, then they are significant

Ex: 1000. m = 4 SFs

NOTE: If there is no decimal after the zeros, then they are not significant.

Ex: 1000 m = 1 SF

how many significant figures are in each of the following measurements
How many significant figures are in each of the following measurements?

1) 76.23 g

Ans. 4 SF’s

2) 6,330. m

Ans. 4 SF’s

3) 6330 m

Ans. 3 SF’s

4) .00225 mg

Ans. 3 SF’s

5) .020030 mg

Ans 5 SF’s

rules for rounding sfs
Rules for Rounding SFs
  • If the digit following the last digit to be retained is: *examples rounded to 3 SF’s

1. Greater than 5 : increase by 1

EX/ 55.49 g = 55.5 g

2. Less than 5 :Stay the same

EX/ 18.62 g = 18.6 g

3. 5, followed by a nonzero digit: increase by 1

EX/ 12.257 g = 12.3 g

rules rounding continued
Rules rounding continued

4.) 5, not followed by nonzero digit, and preceded by an odd digit

Rule : increase by 1 “round up”

Ex/ 4.635 g = 4.64 g ( 3 sig figs)

5.) 5, not followed by nonzero digit, preceded by an EVEN digit. Rule: stays the same

Ex/ 78.65 mL = 78.6 mL

rules for calculations with sf s
Rules for Calculations with SF’s
  • Adding or Subtracting Significant Figures
  • When adding or subtracting decimals, the answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right.
  • Ex: 5.44 m  2 SFs to right of decimal
  • - 2.6103 m  4 SFs to right of decimal
  • 2.8297 m
  • final answer is 2.83 m
slide14

Multiplying or Dividing Significant Figures

  • When multiplying or dividing with SFs, the answer can have no more SFs than are in the measurement with the fewest number of SFs.
  • Ex: m = DV

2.4 g/mL x 15.82 mL = 37.968 g

Final answer is 38 g with 2 SFs

slide15

Scientific Notation are the writing of very large or small numbers in the form M x 10n, where M is a number greater than or equal to one, but less than 10, and n is a whole number.

  • Ex: 5 200 000 000 g = 5.2 x 109 g
  • Ex: 0.000 023 g = 2.3 x 10-5 g
practice do these examples in your notes
Practice: do these examples in your notes

4.5 x 104g (4.5 x 104cm)(2.7 x 103cm)

+2.7 x 103g

4.5 x 104g / 2.7 x 103mL

international system of units
International System of Units

Called the SI system (or Metric System)

  • -established in France 1790 (SystemeInternationaled’Unites)
  • -1960 revised for International scientific agreement.
  • -SI system is simple because it is based on factors of 10 
7 base units
7 Base Units
  • Quantity MeasuredUnitabbreviation
  • length meter m
  • mass gram g
  • time second s
  • electric current ampere A
  • temperature Kelvin K
  • amount of substance mole mol
  • luminous intensity (light) candela cd
si prefixes
SI Prefixes

k kilo 1000x’s (1 km = 1000 m)

h hecto 100x’s (1 hm = 100 m)

dadeka 10x’s (1 dam = 10 m)

Base Units (m, g, s, mol, cd, A, K)

d deci 1/10 (10 dm = 1 m)

c centi 1/100 (100 cm = 1 m)

m milli 1/1000 (1000 mm = 1 m)

converting one unit to another
Converting one unit to another

Two ways:

  • 1. Use a conversion factor that expresses the relationship between the units.
  • Ex/ 1 m = 100 cm
  • Two conversion factors: ___1 m__ or __100 cm__

100 cm 1 m

  • How many meters in 550 cm?
  • 550 cm x __1 m____ = 5.5 m

100 cm

slide22

2. Convert units by shifting the decimal place.

  • King Henry’s daughter begins dance class Monday.
  • 550 cm = __________m
  • 6.77 hg = __________ dg
  • k h da B d c m
  • Start with given units and jump to desired units. Move decimal same direction as number of jumps.
metric conversions practice
Metric Conversions practice:

Copy this practice and turn in when completed:

1) 40.0 m= _________cm

2) 40.0 m= __________km

3) 32.41 m= _________dam

4) 32.41 m= __________hm

5) .005 m= ___________mm

6) .005 km= ___________m

7) .005 km= __________dm

8) .005 mm= __________dam

9) 16 km=___________dam

10) 16 km ___________cm

metric conversions practice key
Metric Conversions practice: Key
  •  40.0 m= __4.00 x 103__cm (4000 cm)
  • 40.0 m= ___.0400____km
  • 32.41 m= ___3.241__dam
  • 32.41 m= ___.3241___hm
  • .005 m= ______5____mm
  • .005 km= _____5_____m
  • .005 km= ___5 x 101__dm (50 dm)
  • .005 mm= _5 x 10-7___dam (.0000005)
  • 16 km=____1600___dam
  • 16 km _1600000 or 1.6 x 106_cm
derived units
Derived Units:

come from base units (multiplying or dividing base units)

For example: Volume (mL) is considered a derived unit.

Using water to fill a cube that is 1 cm on each side:

Volume= l x w x h

vol= 1 x 1 x 1= 1cm3

1 cm3= 1 mL in a graduated cylinder.

1 L = 1000 mL = 1000 cm3

*The mass of 1 cm3 of water equals 1 gram as well.

1 cm3= 1 mL= 1g