Metric Units and Measurement

Units of Measurement Why do we need a “standard” unit of Measurement? – Report Data that can be reproduced Base Units – Time = Seconds (s) – Length = meter (m) – Mass = kilogram (kg) – Volume = space occupied by an object Liter (L)

Metric Units

Derived Units Continued or Now What are the units for the following? – Mass = ? Grams or g – Volume = ? mL or cm 3 Now… Insert them into the formula!

Derived Units Now What are the units for the following? – Mass = ? Grams or g – Volume = ? mL or cm 3 = Combination of base units Example: Density Density = Mass Divided by Volume – How would we write this? Use symbols.

Density So… Density is the Ratio of Mass to Volume.

Determining Volume Here is an odd shaped Object… How would you find the volume if you couldn’t take any measurements? Water displacement that’s how… What happens when you get into a bath tub that is filled to the top with water? – That’s right it over flows! Why.. Water displacement

Water Displacement Let’s take our object And a graduated Cylinder filled with some water … enough to cover the object … but not completely filled (remember what happened to the bath tub!)

Water Displacement and Volume What would happen if we placed our object … into the graduated cylinder? The Water level starts at.. – 46 mL Ends at 66 mL What’s the difference… – 20 mL – That’s the volume of the object

Using the Density formula answer the following questions. A piece of metal with a mass of 147g is placed in a 50mL graduated cylinder. The water level rises from 20mL to 41mL. What is the density of the metal? What is the volume of a sample that has a mass of 20g and a density of 4 g/mL?

Units All measurements start with the base unit – Length is m or meters – Volume is L or liters – Mass is g or grams How ever… what if the object is less than the base unit? Let’s look at length or meters (m) 1 meter

Units continues Each unit (m, L, g) is broken down into parts of 10 Lets break this meter stick into 10 parts 1 meter Each part is 1/10 th of a meter Each part is called a decimeter or dm So… what is the length of this nail? – 4 dm or 4 decimeters

This is 1 dm This is 1 cm This is 1 mm

Prefixes Used with SI Units

Examples Centimeter = ? – 100 th of a meter or.01 or Kilometer = ? – 1000 meters or 10 3 Millimeter – 1000 th of a meter / or.001 / or 10 -3

Temperature What is the SI Unit of Temperature? – Kelvin (K) 273 K = freezing point of water 373 K = boiling point of water What’s the difference between the two? – 100 degrees What is Celsius? – Temperature measurement based on 0 o – 100 o C We will always convert Celsius to Kelvin, unless told not to.

Converting Kelvin to Celsius Convert - Celsius to Kelvin – o C (what you measured) K = Kelvin Convert – Kelvin to Celsius – o K (what you measured) – 273 K = o Celsius Convert the following to Kelvin – 357 o C – -39 o C Convert the following to Celsius – 266 K – 332 K

Activity – miniLAB - Density Follow the directions on page 15 of your book We will be doing a lab write up on this lab.

NEXT CLASS: Chapter 2:1 / 2:2 Homework: WB 2:1 / 2:2 Quiz 3: Day 5 (Chapter 2:1 / 2:2)

TODAY: Chapter 2:2 / 2:3 DAY 5 – NO QUIZ!!! – Density LAB – Sections 2 AND 3 – Next Class Sections 2 AND 3 – HW: Sections 2 and 3 Homework: – Homework: WB 2:2 / 2:3 Quiz 3: Day 6 (Chapter 2:2 / 2:3)

Density Lab Materials; – Cork stopper, Rubber stopper, Nut and bolt – Graduated cylinder, water Formula: D=M/V Data Table: MASSVOLUMEDENSITY Final (mL)Initial (mL)Volume Cork Stopper Rubber Stopper Nut & Bolt

Convert to Scientific Notation Pretest 134,000 5,

Scientific Notation What's the goal of Scientific Notation? – Condense the number that is written Example: What would you rather write – Or – 4.56 x

Rules of Scientific Notation It’s all about the decimal point! And power of 10! Example:645,000 1 st … move the decimal point so one # is to the left of it nd … place “x 10” to the right x 10 3 rd … count the number of spaces you moved the decimal point X 10 5 Almost Done!

X 10 5 Now get rid of the zeros 6.45 X 10 5 Rules: #1..moving the decimal point to the left… the exponent gets bigger #2… moving the decimal point to the right… the exponent gets smaller 64.5 X 10… what's the exponent 6.45 X 10 4

Adding Exponents Rules: 1 st … exponents need to be the same. Move the decimal point until the two numbers have the same exponent 2 nd … add OR subtract the numbers… not the exponents. Example: Add the following #s…Follow the Rules 6.45 x x 10 4 Answer: 6.76 x 10 5

Practice problems pg 32 Addition and Subtraction Every problem

Pretest Multiply (2 x 10 3 ) x (3 x 10 2 ) Divide (9 x 10 8 ) ÷ (3 x )

Multiplying / Dividing Multiplying Rules: – 1 st … multiply the numbers – 2 nd … add the exponents Dividing Rules – 1 st … divide the numbers – 2 nd … subtract the exponents

Practice Problems pg 33 Multiply (2 x 10 3 ) x (3 x 10 2 ) = Divide (9 x 10 8 ) ÷ (3 x ) =

Conversions Rules: 1 st … write down what you know 2 nd … write down what you want to know 3 rd … what conversion factor are you going to use to get there? Convert 48km to meters (factor: 1km=1000meters) =______m or 48000

Types of Measurements Precise vs. Accurate

Percent Error The Accepted value is a known value Error = Accepted - Measured

% error example The accepted density for copper is 8.96g/mL. Calculate the percent error for each of these measurements g/mL 8.92 g/mL 9.00 g/mL 8.98 g/mL 1.11%.45%.22%

Significant Figures or Sig Figs Tells the how precise the measurement is Example: Which is more precise?  3.5 or 3.52g

Rules for Sig Figs – pg Non-zero umbers are always significant 2.Zeros between non-zero numbers are always significant 3.All final zeros to the right of the decimal place are significant. 4.Zeros that act as placeholders are NOT significant. Convert quantities to scientific notation to remove the placeholders. 5.Counting numbers and defined constants have an infinite number of significant figures.

Examples – use your rules Which numbers are significant?  72.3  60.5  6.20   4320  Help yourself out – convert to Scientific Notation

Rounding Numbers – pg 40 1.If the digit to the immediate right of the last sig fig is less than five, do not change the last sig fig. 2.If the digit to the immediate right of the last sig fig is greater than five, round up the last sig fig 3.If the digit to the immediate right of the last sig fig is equal to five and is followed by a nonzero digit, round up the last sig fig. 4.If the digit to the immediate right of the last sig fig is equal to five and is not followed by a nonzero digit, look at the last sig fig. if it is an odd digit, round it up. If it is an even digit, do not round up