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Measurements and Calculations. Chapter 2. Units of Measurement. Measurements involve NUMBER and UNIT Represent a quantity : has magnitude, size, or amount Gram = unit of measurement Mass = quantity. Units of Measurement. Scientists around the world agree on one system…

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units of measurement
Units of Measurement
  • Measurements involve NUMBER and UNIT
  • Represent a quantity: has magnitude, size, or amount
  • Gram = unit of measurement
  • Mass = quantity
units of measurement3
Units of Measurement
  • Scientists around the world agree on one system…
    • International System of Units (le Systeme International d’Unites)
    • SI units
    • Built from seven base units
units of measurement6
Units of Measurement
  • Metric Prefixes – make units easier to use
  • Make the unit smaller or larger
  • Unit = prefix + base unit
  • Table pg. 35
slide7
Mass
  • Measures quantity of matter
  • SI unit: kilogram, kg
  • ______ kg = _____ g
  • gram used for smaller masses
  • Weight: measure of gravitational pull
length
Length
  • SI unit: meter, m
  • Longer distances: kilometer, km
  • _______ km = _______ m
  • Shorter distances: centimeter, cm
  • _______ m = ________ cm
volume
Volume
  • SI unit: m3
  • A derived unit: combination of base units by multiplying or dividing
  • SI unit for Area: l x w = m x m = m2
  • Volume: l x w x h = m x m x m = m3
  • Also: liters (L), mL, dm3 and cm3
  • 1 L = 1 dm3 = 1000mL = 1000 cm3
scientific notation
Scientific Notation
  • Put the numbers in the form

a x 10n

  • a has one # to left of decimal
  • If # is bigger than 1  + exponent
  • If # is less than 1  - exponent
scientific notation12
Scientific Notation
  • Review: Write in scientific notation

32,700

0.0003412

3.901 x 10-6

4.755 x 108

significant figures sig figs

1

2

3

4

5

Significant Figures (sig figs)
  • How many numbers mean anything?
  • When we measure, we can (and do) always estimate between the smallest marks.
significant figures sig figs14
Significant figures (sig figs)
  • Better marks better estimate.
  • Last number measured actually an estimate

1

2

3

4

5

sig figs
Sig Figs
  • What is the smallest mark on the ruler that measures 142.15 cm?
  • 142 cm?
  • 140 cm?
  • Does the zero mean anything? (Is it significant?)
  • They needed a set of rules to decide which zeroes count.
sig figs16
Sig Figs.
  • 405.0 g
  • 4050 g
  • 0.450 g
  • 4050.05 g
  • 0.0500060 g
sig figs17
Sig Figs
  • Only measurements have sig figs.
  • Counted numbers are exact – infinite sig figs
  • A dozen is exactly 12
  • Conversion factors: 100 cm = 1 m
problems
Problems
  • 50 has only 1 significant figure
  • if it really has two, how can I write it?
  • Scientific notation
  • 5.0 x 101

2 sig figs

  • Scientific Notation shows ALL sig figs
rounding rules
Rounding rules
  • Round 454.62 to four sig figs
    • to three sig figs
    • to two sig figs
    • to one sig fig
calculations
Calculations
  • 165.86 g + 4.091g - 140 g + 27.32 g
  • (35.6 L + 2.4 L) / 4.083 =
  • 2.524 x (16.408 m – 3.88 m) =

Answers: 57g 9.31 L 31.62 m

sig figs21
Sig figs.
  • How many sig figs in the following measurements?
  • 458 g
  • 4085 g
  • 4850 g
  • 0.0485 g
  • 0.004085 g
  • 40.004085 g
density
Density
  • Density = mass D = m

volume V

  • Units: g/cm3 or g/mL but SI unit is kg/m3
  • derived unit
  • Used to identify substances
  • Varies with temperature
  • As temp. increases density…
density examples
Density Examples
  • If a metal block has a mass of 65.0 grams and a volume of 22 cubic centimeters, what is the density of the block?
  • D = m

V

  • D = 65.0 g = 3.0 g/cm3

22 cm3

density examples25
Density Examples
  • Aluminum has a density of 2.7 g/cm3. What volume of aluminum has a mass of 60 grams?
  • D = M

V

20 cm3

density examples26
Density Examples
  • Gold has a density of 19.3 g/cm3. A block of metal has a mass of 80 g and a volume of 12 cm3. Could this block be a piece of gold?
  • No, because this block has a density of 7 g/cm3s
unit conversions28
Unit Conversions
  • Given information in one unit  need to find the equivalent in another unit
  • Identify what’s given
  • Organize plan of attack
  • Carry out plan WITH UNITS!!
conversion factors
Conversion factors
  • “A ratio of equivalent measurements.”
  • Start with two things that are the same.

1 m = 100 cm

  • Can divide by each side to come up with two ways of writing the number 1.
slide30

1 m

100 cm

100 cm

100 cm

Conversion factors

=

slide32

1 m

=

100 cm

1 m

1 m

Conversion factors

1 m

=

1

100 cm

slide33

Conversion factors

1 m

=

1

100 cm

=

100 cm

1

1 m

conversion factors34
Conversion Factors
  • Unique way of writing the number 1.
  • Does NOT change the VALUE, it changes the UNITS.
write the conversion factors for the following
Write the conversion factors for the following
  • kilograms to grams
  • feet to inches
  • 1 L = 1 dm3 = 1000mL = 1000 cm3
let s see how they work
Let’s See How They Work
  • We can multiply by a conversion factor creatively to change the units .
  • 13 inches is how many yards?
let s try some
Let’s Try Some!
  • 323 mm = _____ nm
  • 3.2 miles = _____ in
  • 250 gallons = _____ mL
  • 15 days = _______ min
derived unit conversions
Derived Unit Conversions
  • 54.3 cm3 = ______ m3
  • 7.54 ft2 = _______ in2
derived unit conversions40
Derived Unit Conversions
  • 125.3 m/s = ______ mi/hr
  • 625 g/mL = ______ kg/m3
  • 100 km/hr = ______ mi/hr
making good measurements
Making Good Measurements
  • We can do 2 things:
  • Repeat measurement many times

- reliable measurements get the same number over and over

- this is PRECISE

making good measurements43
Making Good Measurements

2. Test our measurement against a “standard”, or accepted value

- measurement close to accepted value is ACCURATE

Video - 46

measurements are uncertain
Measurements are Uncertain
  • Measuring instruments are never perfect
  • Skill of measurer
  • Measuring conditions
  • Measuring always involves estimation
    • Flickering # on balance
    • Between marks on instrument
error
Error
  • Probably not EXACTLY 6.35 cm
  • Within .01 cm of actual value.
  • 6.35 cm ± .01 cm
  • 6.34 cm to 6.36 cm
calculating percent error
Calculating Percent Error
  • Compares your measurement to accepted value
  • Negative if measurement is small
  • Positive if measurement is big
calculating percent error48
Calculating Percent Error
  • What is the % error for a mass measurement of 17.7g, given that the correct value is 21.2g?
direct proportions
Direct Proportions
  • Two quantities are directly proportional if dividing one by the other gives a constant
  • yx “y is proportional to x”
  • Gen. Eqn: y = k

x

  • Ex: mass and volume… constant is…
direct proportions50
Direct Proportions
  • Solve for y: y = k

x

  • Look familiar?
  • Eqn for a straight line: y = mx + b
  • Slope is the constant
inverse proportions
Inverse Proportions
  • Two quantities are inversely proportional if their product is a constant
  • “y is proportional to 1 divided by x”
  • Gen eqn: xy = k
  • Ex: speed and travel time
inverse proportion
Inverse Proportion

Graph is called “hyperbola”

calculations54
Calculations
  • Convert 3.23 x 104 kg to g. Give answer with correct sig. figs.
  • How many miles are in 450,000 in?
calculations55
Calculations
  • What is the mass of an object with a density of 25.98 g/mL and a volume of 4.2 mL?
  • What is the density of a 430 g object that takes up 25.5 cm3?