 # Measurements and Calculations Chapter 2. Units of Measurement Measurements involve NUMBER and UNIT Represent a quantity: has magnitude, size, or amount.

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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… –International System of Units (le Systeme International d’Unites) –SI units –Built from seven base units

SI Base Units

Units of Measurement

Metric Prefixes – make units easier to use Make the unit smaller or larger Unit = prefix + base unit Table pg. 35

Mass Measures quantity of matter SI unit: kilogram, kg ______ kg = _____ g gram used for smaller masses Weight: measure of gravitational pull

Length SI unit: meter, m Longer distances: kilometer, km _______ km = _______ m Shorter distances: centimeter, cm _______ m = ________ cm

Volume SI unit: m 3 A derived unit: combination of base units by multiplying or dividing SI unit for Area: l x w = m x m = m 2 Volume: l x w x h = m x m x m = m 3 Also: liters (L), mL, dm 3 and cm 3 1 L = 1 dm 3 = 1000mL = 1000 cm 3

Derived Units

Scientific Notation Put the numbers in the form a x 10 n a has one # to left of decimal If # is bigger than 1  + exponent If # is less than 1  - exponent

Scientific Notation Review: Write in scientific notation 32,700 0.0003412 3.901 x 10 -6 4.755 x 10 8

Significant Figures (sig figs) How many numbers mean anything? When we measure, we can (and do) always estimate between the smallest marks. 21345

Significant figures (sig figs) Better marks better estimate. Last number measured actually an estimate 21345

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 Figs. 405.0 g 4050 g 0.450 g 4050.05 g 0.0500060 g

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 50 has only 1 significant figure if it really has two, how can I write it? Scientific notation 5.0 x 10 1 2 sig figs Scientific Notation shows ALL sig figs

Rounding rules Round 454.62 to four sig figs –to three sig figs –to two sig figs –to one sig fig

Calculations 1.165.86 g + 4.091g - 140 g + 27.32 g 2.(35.6 L + 2.4 L) / 4.083 = 3.2.524 x (16.408 m – 3.88 m) = Answers: 57g9.31 L31.62 m

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 = massD = m volume V Units: g/cm 3 or g/mL but SI unit is kg/m 3 derived unit Used to identify substances Varies with temperature As temp. increases density…

Density

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/cm 3 22 cm 3

Density Examples Aluminum has a density of 2.7 g/cm 3. What volume of aluminum has a mass of 60 grams? D = M V 20 cm 3

Density Examples Gold has a density of 19.3 g/cm 3. A block of metal has a mass of 80 g and a volume of 12 cm 3. Could this block be a piece of gold? No, because this block has a density of 7 g/cm 3s

Unit Conversions

Given information in one unit  need to find the equivalent in another unit 1.Identify what’s given 2.Organize plan of attack 3.Carry out plan WITH UNITS!!

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.

Conversion factors 100 cm1 m= 100 cm

Conversion factors 1 1 m= 100 cm

Conversion factors 1 1 m= 100 cm =1 m

Conversion factors 1 1 m= 100 cm = 1 m 1

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 kilograms to grams feet to inches 1 L = 1 dm 3 = 1000mL = 1000 cm 3

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! 323 mm = _____ nm 3.2 miles = _____ in 250 gallons = _____ mL 15 days = _______ min

More Unit Conversions More Involved

Derived Unit Conversions 54.3 cm 3 = ______ m 3 7.54 ft 2 = _______ in 2

Derived Unit Conversions 125.3 m/s = ______ mi/hr 625 g/mL = ______ kg/m 3 100 km/hr = ______ mi/hr

Where do these measurements come from? Recording Measurements

Making Good Measurements We can do 2 things: 1.Repeat measurement many times - reliable measurements get the same number over and over - this is PRECISE

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 1.Measuring instruments are never perfect 2.Skill of measurer 3.Measuring conditions 4.Measuring always involves estimation –Flickering # on balance –Between marks on instrument

Estimating Measurements

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 Compares your measurement to accepted value Negative if measurement is small Positive if measurement is big

Calculating Percent Error What is the % error for a mass measurement of 17.7g, given that the correct value is 21.2g?

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 Proportions Solve for y: y = k x Look familiar? Eqn for a straight line: y = mx + b Slope is the constant

Direct Proportion

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 Graph is called “hyperbola”

Calculations Convert 3.23 x 10 4 kg to g. Give answer with correct sig. figs. How many miles are in 450,000 in?

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 cm 3 ?

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