Measurements

Number vs. Quantity A number without a unit is meaningless A number without a unit is meaningless It is 4 long It is 4 long 4 what? 4 what? Scientists use the metric system or SI for le System Internationale d’Units Scientists use the metric system or SI for le System Internationale d’Units Makes sharing data across countries easier Makes sharing data across countries easier

Number vs. Quantity Quantity has a number + unit Quantity has a number + unit UNITS MATTER!!

SI “Base” Units QuantityUnitAbbreviation Lengthmeterm Massgramg TemperaturekelvinK Electric currentampereA Amount of substancemolemol Luminous intensitycandelacd

Measuring length Use a ruler Use a ruler Line up from zero not the end of the ruler Line up from zero not the end of the ruler Numbered divisions are centimeters Numbered divisions are centimeters Small divisions are millimeters Small divisions are millimeters There are 10 millimeters in 1 centimeter There are 10 millimeters in 1 centimeter 01234

Volume Volume – the amount of space occupied by an object Volume – the amount of space occupied by an object Volume (cm 3 )= length x width x height Liter (L) is also a common unit (for liquids) Liter (L) is also a common unit (for liquids) 1 L = 1 quart; about 1/4 of a gallon 1 L = 1 quart; about 1/4 of a gallon 1 mL is about 20 drops of water or 1 sugar cube, 1 mL = 1 cm 3 1 mL is about 20 drops of water or 1 sugar cube, 1 mL = 1 cm 3

Measuring Volume Use a graduated cylinder. Use a graduated cylinder. The water will curve in the cylinder (meniscus). The water will curve in the cylinder (meniscus). Hold it level with your eye. Hold it level with your eye. Read the bottom of the meniscus. Read the bottom of the meniscus. Measures in milliliters mL. Measures in milliliters mL

Used to measure volume of an irregular solid. Used to measure volume of an irregular solid. 1. Fill water to spout. 2. Put object in. 3. Catch water that comes out. 4. Find volume of that water. Water Displacement Tank

Mass Weight is the force of gravity on an object; Mass is the amount of matter. Weight is the force of gravity on an object; Mass is the amount of matter. 1 gram is defined as the mass of 1 cm 3 of water at 4 ºC. 1 gram is defined as the mass of 1 cm 3 of water at 4 ºC. 1 g = 1 paper clip 1 g = 1 paper clip 1 kg = 1 L of water 1 kg = 1 L of water 1 kg = 2.5 lbs 1 kg = 2.5 lbs 1 mg = 10 grains of salt or 2 drops of water. 1 mg = 10 grains of salt or 2 drops of water.

Measuring Mass Use a triple beam balance Use a triple beam balance First balance it at zero. First balance it at zero. Then put item on Then put item on Then move one weight at a time Then move one weight at a time When balanced, add up the weights When balanced, add up the weights

Triple beam Balance

Accuracy and Precision Accuracy - the closeness of a measurement to the accepted value. Accuracy - the closeness of a measurement to the accepted value. Precision – the closeness of a set of measurements of the same quantity, made the same way. Precision – the closeness of a set of measurements of the same quantity, made the same way.

Accuracy Accuracy - the closeness of a measurement to the accepted value. Accuracy - the closeness of a measurement to the accepted value. Ex. 10 pennies have a mass of exactly 30 g; that is the accepted value. Ex. 10 pennies have a mass of exactly 30 g; that is the accepted value. Jan found the mass of 10 pennies; she got 29.8 g. Jan found the mass of 10 pennies; she got 29.8 g. Tom found the mass of 10 pennies; he got 28.6 g. Tom found the mass of 10 pennies; he got 28.6 g. Jan’s measurement is more accurate than Tom’s Jan’s measurement is more accurate than Tom’s because her 29.8 g is closer to 30 g than Tom’s 28.6 g.

Precision Precision – closeness of a set of measurements of the same quantity, made the same way. Precision – closeness of a set of measurements of the same quantity, made the same way. Ex. 10 pennies have a mass of 30 g; that is the accepted value. Ex. 10 pennies have a mass of 30 g; that is the accepted value. Jan measured the mass of 10 pennies 4 times. She got the following set of measurements: Jan measured the mass of 10 pennies 4 times. She got the following set of measurements: 32.3 g, 32.2 g, 32.3 g, 32.4 g 32.3 g, 32.2 g, 32.3 g, 32.4 g These measurements are NOT These measurements are NOT accurate, but these measurements accurate, but these measurements are precise because they are close are precise because they are close to each other. to each other.

Outliers – data points that don’t fit the trend. That point is likely the result of an error.

Derived Units Combination of base units. Combination of base units. Volume - length  width  height Volume - length  width  height 1 cm 3 = 1 mL 1 dm 3 = 1 L Density - mass per unit volume (g/cm 3 ) Density - mass per unit volume (g/cm 3 ) D = MVMV D M V

Density Problem example An object has a volume of 825 cm 3 and a density of 13.6 g/cm 3. Find its mass. An object has a volume of 825 cm 3 and a density of 13.6 g/cm 3. Find its mass. GIVEN: V = 825 cm 3 D = 13.6 g/cm 3 M = ? WORK : M = DV M = (13.6 g/cm 3 )(825cm 3 ) M = 11,220 g D M V

Density Problem 1 1) A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/mL V = ? M = 25 g D M V WORK : V = M D V = 25 g 0.87 g/mL V = 28.7 mL

Density Problem 2 2) You have a sample with a mass of 620 g & a volume of 753 cm 3. Find density. GIVEN: M = 620 g V = 753 cm 3 D = ? D M V WORK : D = M V D = 620 g 753 cm 3 D = 0.82 g/cm 3

Metric System Measurements have two parts Measurements have two parts Base unit and prefix Base unit and prefix Prefixes multiply or divide the base units by multiples 10 Prefixes multiply or divide the base units by multiples 10 Prefixes are the same for all units Prefixes are the same for all units

SI Unit Prefixes SI Unit Prefixes mega-M10 6 deci-d10 -1 centi-c10 -2 milli-m10 -3 PrefixSymbolFactor micro-  nano-n10 -9 pico-p kilo-k10 3

SI Prefix Conversions SI Prefix Conversions mega-M10 6 deci-d10 -1 centi-c10 -2 milli-m10 -3 PrefixSymbolFactor micro-  nano-n10 -9 pico-p kilo-k10 3 move decimal left move decimal right

Prefix Conversions Mili m 1 Unit Centi c Deci d 10 1 deka dk 10 2 hecta h 10 3 kilo k King Henry danced merrily down central main. King Henry died Monday drinking chocolate milk. Move the decimal in the direction & number of spaces as indicated in the above chart.

Metric Conversion Summary To go from a large unit to a smaller unit: To go from a large unit to a smaller unit: MOVE THE DECIMAL TO THE RIGHT To go from a small unit to a larger unit: To go from a small unit to a larger unit: MOVE THE DECIMAL TO THE LEFT

SI Prefix Conversions 1. Find the difference between the exponents of the two prefixes. 2. Move the decimal that many places. To the left or right?

= SI Prefix Conversions NUMBER UNIT NUMBER UNIT 532 m = _______ km 0.532

Metric conversions A common race is the 5 K, which is 5 km. How many meters is this? A common race is the 5 K, which is 5 km. How many meters is this? Unit given -km Unit given -km Unit wanted –m Unit wanted –m The unit gets smaller, so the number must get bigger The unit gets smaller, so the number must get bigger 1000 m = 1 km 1000 m = 1 km

Conversion Problems 1) 20 cm = ______________ m 2) A = ______________ mA 3) 45  m = ______________ nm 4) 805 dm = ______________ km ,000 32

Dimensional Analysis The “Factor-Label” Method The “Factor-Label” Method Units, or “labels” are canceled, or “factored” out Units, or “labels” are canceled, or “factored” out

Dimensional Analysis Steps: Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer.

Dimensional Analysis Problem Lining up conversion factors: Lining up conversion factors: 1 in = 2.54 cm 2.54 cm 1 in = 2.54 cm 1 in 1 in = 1 1 = 1 in = 2.54 cm

Dimensional Analysis Your European hairdresser wants to cut your hair 8 cm shorter. How many inches will he be cutting off? Your European hairdresser wants to cut your hair 8 cm shorter. How many inches will he be cutting off? 8 cm 1 in 2.54 cm = 3.15 in  cmin

Dimensional Analysis How many milliliters are in 1 quart of milk? How many milliliters are in 1 quart of milk? 1 qt 1 L qt = 946 mL qtmL 1000 mL 1 L

Dimensional Analysis 5) Assume your mass is 55 kg. How many pounds do you weigh? 55 kg 2.2 lb 1 kg = 121 lb kglb

Dimensional Analysis 6) How many feet long is a 5K (5 km) race? 5 km 1 mi km = 16,408 ft kmft 5280 ft 1 mi

Dimensional Analysis 7) How many grams does a 10-lb. bag of potatoes weigh? 10 lb 1 kg 2.2. lb = 4545 g lbg 1000 g 1 kg

Dimensional Analysis 8) Taylor football needs 550 cm for a 1st down. How many yards is this? 550 cm 1 in 2.54 cm = 6.01 yd cmyd 1 ft 12 in 1 yd 3 ft

Types of Graphs Line Graph Line Graph shows the relationship between 2 variables shows the relationship between 2 variables Dependent Variable Independent Variable

Types of Graphs Bar Graph Bar Graph shows information collected by counting shows information collected by counting

Types of Graphs Pie Graph Pie Graph shows distribution of parts within a whole quantity shows distribution of parts within a whole quantity

Graphing & Density Mass (g) Volume (cm 3 )