Units and Measurements

Units and Measurement Cue column summary Notes

Learning Objectives I can define SI base units for time, length, mass, and temperature. I can explain how adding a prefix changes a unit. I can convert between units using dimensional analysis. I can compare the derived units for volume and density.

SI Base Units and Prefixes

System International Unites (SI) The International System of Units (SI) defines seven units of measure as a basic set from which all other SI units are derived A base unit is a defined unit in a system of measurement that is based on an object or event in the physical world. QuantityBase Unit Timeseconds (s) Lengthmeter (m) Masskilogram (kg) Temperaturekelvin (K) MEMORIZE THESE

Temperature Three different temperature scales are in common use: – Celsius – Kelvin – Fahrenheit

Temperature The SI base unit for temperature is the kelvin (K). On this scale, water freezes at K and boils at K. Absolute zero – 0K (zero Kelvin) is the point at which the movement of particles is at its slowest.

Temperature Fahrenheit – water freezes 32°F – Water boils 212°F Celsius – Water freezes 0°C – Water boils 100°C

SI Prefixes PrefixSymbolValuePower of 10 Equivalent Kilok g, s, m110 0 Decid Centic Millim1, Microµ1,000, Nanon1,000,000, MEMORIZE THESE! There will be quiz on this TOMORROW

SI Prefixes To read the chart… – There are ________ kilograms in a gram – There are ________ decigrams in a gram – There are ________ centigrams in a gram – There are _________ milligrams in a gram – There are _________ micrograms in a gram – There are _________ nanograms in a gram

SI Prefixes Here is a mnemonic device to help you remember the order of the prefixes: Kids Don’t Usually Count M & Ms, Nope! (they eat them!) kilo, Unit (base unit), deci, centi, milli, micro, nano

Dimensional Analysis

Team Materials When I say GO… Team member number 1 collects a team tub for his/her team. Team member number 2 collects enough white boards for each team member. Team member number 3 passes out enough white board markers to everyone. Team member number 4 passes out enough felt pieces (erasers) for everyone.

Numbered Heads Together 1.Teacher asks a question or poses a problem. 2.Team members privately write their answers. a.Flip whiteboards over when you are ready 3.Students stand up and “put their heads together, showing answers, discussing, and teaching each other. 4.Students sit down when EVERYONE can explain how to solve the problem. 5.Teacher calls a number. Students with that number answer simultaneously using Answer Board Share.

Pizza Party! How many pizzas would we need if each person in class eats three slices and each pizza had 8 slices? ____ students 3 slices 1 student 1 pizza 8 slices

Dimensional Analysis Dimensional analysis is a method used to convert from one unit to another using conversion factors. A conversion factor is a ratio of equivalent values having different units obtained from an equality. Conversion factor Conversion factor

Conversion Factor

Learning Check Write equalities and conversion factors for each pair of units. A.Liters (L) and milliliters (mL) B.Hours (hr) and minutes (min) C.Meters (m) and kilometers (km) D.Seconds (s) and microseconds (µs)

Dominos Think of dimensional analysis like matching up dominos. Your conversion factors are the dominos. You want to match your dominos up so that your units cancel and you end up with the unit you were asked to find.

Guide to Problem Solving (GPS) Step 1 – Identify the given and needed units. Step 2 –State the equalities and conversion factors (make your dominos) to cancel units. Step 3 –Set up problem to cancel units. (match up your dominos) Step 4 –calculate answer (numbers next to each other are multiplied, numbers underneath are divided).

Dimensional Analysis Foldable Explanation of Step Identify the given and needed units. Example of Each Step If our class of ___ students had a pizza party… Step 1 Step 2 Step 3 Step 4 Outside foldable Inside Foldable Homework: Finish the foldable & Revise your homework from Friday

Examples A standard aspirin tablet contains 324 mg of aspirin. How many grams of aspirin are in a standard aspirin tablet? Step 1: given - needed - Step 2: ____g = _____mg or Step 3 & 4: 324 mg1g 1000 mg 1g 1000 mg 1g 1000 mg _________g of aspirin

Identify given and needed units. A standard aspirin tablet contains 324 mg of aspirin. How many grams of aspirin are in a standard aspirin tablet? State the equalities and conversion factors to cancel units. Set up problem to cancel units. calculate answer

Example Analysis shows the presence of 203 µg of cholesterol in a sample of blood. How many grams of cholesterol are present in this blood sample?

Example How many eight-packs of water would you need if 32 people were attending and you wanted to have enough water for each person to have two bottles of water?

Domino Activity 1.Person #3 pass out scissors to all team members. 2.Person #1, write your team color on the “name” line. 3.Person #4, cut out domino pieces and hand out a piece for each team member to cut. 4.Everyone STANDS UP and works together to cut out domino pieces. NOBODY may sit down until ALL pieces are cut.

Domino Activity 1.Person #____ starts off by identifying the needed and given units. 2.Person #____ states the equalities and conversion factors needed to solve the problem. 3.Person #___ sets the problem up to cancel units. 4.Person #___ performs the calculation. 5.Next group member checks work before passing paper on to start over.

Derived Units

A unit that is defined by a combination of base units is called a derived unit. Examples of derived units: – Volume – Density

Volume Volume is the space occupied by an object. – V = l x w x h When each dimension is given in meters, the calculated volume has units of cubic meters (m 3 ) The derived SI unit for volume is the cubic meter.

Volume A liter (L) is equal to one cubic decimeter (dm 3 ). – 1L = 1dm 3 For smaller quantities of liquid in the laboratory, volume is often measured in cubic centimeters (cm 3 ) or milliliters (mL). 1 mL = 1 cm 3

Volume The volume of an irregularly shaped solid can be determined using the water displacement method. Determine initial and final volume. Subtract initial volume from final volume to get the volume of the object. – Example: 225 mL – 200 ml = 25mL Initial Volume Final Volume

Density Write both of these in your notes!

Example 116 g of sunflower oil is used in a recipe. The density of the oil is g/mL. What is the volume of the sunflower oil in mL?

Example When a piece of aluminum is placed in a 25-mL graduated cylinder that contains 10.5 mL of water, the water level rises to 13.5 mL. The density of aluminum is 2.7 g/mL. What is the mass of the aluminum?

RoundTable Density 1.Person #____ starts off by identifying the needed and given units. 2.Person #____ writes the equation needed to solve the problem. 3.Person #___ performs the substitutions. 4.Person #___ performs the calculation recording the answer to the correct number of significant figures and with correct units. 5.Next group member checks work before passing paper on to start over.

Density Equation Foldable Define volume Equation for volume Units of volume Define volume Equation for volume Units of volume Define mass Equation for mass Units of mass Define mass Equation for mass Units of mass Define density Equation for density Units of density (there are two) Define density Equation for density Units of density (there are two)

Finding Density Foldable Picture & ExampleExplanation Picture & Example

Summary SI measurement units allow us to report data to others. Adding prefixes to SI units extends the range of possible measurements. Dimensional analysis uses conversion factors to convert from one unit to another. Volume and density have derived units.