Metric System of Measurement

Metric System of Measurement
What is the metric system?

Why do we have to learn this?
Standard: 8Sa: you will demonstrate an understanding of technological design and scientific inquiry, including process skills, mathematical thinking, controlled investigative design and analysis, and problem solving. Objectives: You will convert, apply, and arrange metric conversion units You will use, apply, and evaluate metric prefixes, and base units to labs You will apply unit factor analysis, scientific notation, and significant figures to metric calculations. You will apply the ladder method and division and multiplication by 10 to calculate and convert metric units.

The system of measurement that we use is based on the following.
An inch represents the width of a thumb. Copyright © 2010 Ryan P. Murphy

The gallon, the basic English unit of volume, was originally the volume of eight pounds of wheat.
Copyright © 2010 Ryan P. Murphy

The mile is a Roman unit, originally defined to be the length of 1000 paces of a Roman legion.

Acre was originally the size of a field that a farmer could plow in a single day.

Countries that don’t use the metric system as their standard

Countries that don’t use the metric system as their standard.

Countries that use the metric system…

The countries colored in red are the ones that don’t use the metric system.

The countries colored in red are the ones that don’t use the metric system.
The United States Copyright © 2010 Ryan P. Murphy

Liberia, No official system of measurement
The countries colored in red are the ones that don’t use the metric system. The United States Liberia, No official system of measurement Copyright © 2010 Ryan P. Murphy

Liberia, No official system of measurement
The countries colored in red are the ones that don’t use the metric system. The United States Liberia, No official system of measurement Burma – The Burmese Unit Copyright © 2010 Ryan P. Murphy

Every other country in the world uses the Metric System

Every other country in the world uses the Metric System
Why does the United States use a poor system of measurement?

Pride?

Patriotism? Pride?

Patriotism? Pride? Lazy?

Patriotism? Pride? Lazy? $

Patriotism? Pride? Lazy? $ Lack of Interest?

Patriotism? Pride? Lazy? $ Education? Lack of Interest?

Patriotism? Pride? Lazy? $ Sports? Education? Lack of Interest?

$ Patriotism? Pride? Change? Lazy? Sports? Education?
Lack of Interest?

Even England uses the metric system over the Old English System that we use.

The American System of Measurement, or Old English System is good because it is rooted in history.

The American System of Measurement, or Old English System is good because it is rooted in history. We should still study it as part of history, but that is it. Adios Cheesy System! Copyright © 2010 Ryan P. Murphy

What are the odds of this?

“False Start.” “4.57 Meter Penalty” “Repeat 1st Down.”

Link to the Powers of 10 portion of video.
IMAX Cosmic Voyage Link to the Powers of 10 portion of video. Copyright © 2010 Ryan P. Murphy

How many kilometers away from the earth is the sun?

Metric System The Metric system of measurement was created about two hundred years ago by a group of French scientists to simplify measurement.

Math and Units Math- the language of Science
SI Units – International System Meter m Mass g Time s Volume L Temperature oC, Kelvin K

Video! The U.S. Customary System vs. The Metric System.

The International System of Units (SI) also known as the metric system.

Activity! Visiting an online Metric Converter.
We will learn to do a few conversions. Copyright © 2010 Ryan P. Murphy

Length: Base unit in the metric system is the Meter (m)
The measured distance from one end to the other of an object. Base unit in the metric system is the Meter (m)

English vs. Metric Units
Which is longer? A. 1 mile or 1 kilometer B. 1 yard or 1 meter C. 1 inch or 1 centimeter 1.6 kilometers 1 mile 1 yard = meters 1 inch = 2.54 centimeters Left Image: Right Image:

Click the image to watch a short video about the meter.
Metric Units km m cm mm The basic unit of length in the metric system in the meter and is represented by a lowercase m. Standard: The distance traveled by light in absolute vacuum in 1⁄299,792,458 of a second. Metric Units 1 Kilometer (km) = 1000 meters 1 Meter = 100 Centimeters (cm) 1 Meter = 1000 Millimeters (mm) Click the image to watch a short video about the meter. Which is larger? A. 1 meter or 105 centimeters B. 4 kilometers or 4400 meters C. 12 centimeters or 102 millimeters D millimeters or 1 meter

Measuring Length How many millimeters are in 1 centimeter?
1 centimeter = 10 millimeters How many millimeters are in 1 centimeter? What is the length of the line in centimeters? _______cm What is the length of the line in millimeters? _______mm What is the length of the line to the nearest centimeter? ________cm HINT: Round to the nearest centimeter – no decimals. Ruler:

1 meter (1m)

1 meter (1m) or the length of a baseball bat

About the thickness of a dime
1 millimeter (1 mm) About the thickness of a dime

1 centimeter (1 cm)

OR About the length of 10 football fields
1 kilometer (1 km) OR About the length of 10 football fields

One Meter

1 meter has 100 centimeters

1 meter has 100 centimeters 10 mm 100

1 meter has 1000 millimeters 10 mm

1 meter has 1000 millimeters 10 mm 1000

Mass: Base unit in the metric system is the Gram.
A quantity of matter. Base unit in the metric system is the Gram. Video Link

1 pound = grams Which is larger? 1. 1 Pound or 100 Grams 2. 1 Kilogram or 1 Pound 3. 1 Ounce or 1000 Milligrams 1 kilogram = 2.2 pounds 1 ounce of gold = 28,349.5 milligrams

1 pound = grams Which is larger? 1. 1 Pound or 100 Grams 2. 1 Kilogram or 1 Pound 3. 1 Ounce or 1000 Milligrams 1 kilogram = pounds 1 ounce of gold = 28,349.5 milligrams

Metric Units kg g cg mg Kilogram Prototype Mass refers to the amount of matter in an object. The base unit of mass in the metric system in the kilogram and is represented by kg. Metric Units 1 Kilogram (km) = 1000 Grams (g) 1 Gram (g) = 1000 Milligrams (mg) Click the image to watch a short video about mass. Which is larger? A. 1 kilogram or 1500 grams B milligrams or 1 gram C. 12 milligrams or 12 kilograms D. 4 kilograms or 4500 grams Kilogram Prototype Image -

_______ + ______ + _______ = ________ g
Measuring Mass We will be using triple-beam balances to find the mass of various objects. The objects are placed on the scale and then you move the weights on the beams until you get the lines on the right-side of the scale to match up. Once you have balanced the scale, you add up the amounts on each beam to find the total mass. What would be the mass of the object measured in the picture? _______ + ______ + _______ = ________ g Top Image: Bottom Image:

Measuring Mass – Triple-Beam Balance
1st – Place the film canister on the scale. 2nd – Slide the large weight to the right until the arm drops below the line. Move the rider back one groove. Make sure it “locks” into place. 3rd – Repeat this process with the top weight. When the arm moves below the line, back it up one groove. 4th – Slide the small weight on the front beam until the lines match up. 5th – Add the amounts on each beam to find the total mass to the nearest tenth of a gram. Click here to try an online activity.

1 gram (1 g) or the mass of a paperclip

About the mass of a grain of sand
1 milligram (1 mg) About the mass of a grain of sand

1 kilogram (1 kg)

Mass vs. Weight Weight is a force based on the amount of gravitational pull. Weight Activity Mass Quick Lab video

Volume / Capacity Base unit in the metric system is the Liter.
Space included within limits as measured Base unit in the metric system is the Liter.

Which is larger? A. 1 liter or 1 gallon B. 1 liter or 1 quart C. 1 milliliter or 1 fluid ounce 1 fl oz = ml 1 12-oz can of soda would equal approximately 355 ml. 1 quart = liters 1 gallon = 3.79 liters It would take approximately 3 ¾ 1-liter bottles to equal a gallon.

Which is larger? A. 1 liter or 1 gallon B. 1 liter or 1 quart C. 1 milliliter or 1 fluid ounce 1 fl oz = ml 1 12-oz can of soda would equal approximately 355 ml. 1 gallon = 3.79 liters It would take approximately 3 ¾ 1-liter bottles to equal a gallon. 1 quart = liters

Click the image to watch a short video about volume.
Metric Units kL cL mL L Volume is the amount of space an object takes up. The base unit of volume in the metric system in the liter and is represented by L or l. Standard: 1 milliliter is equal to one cubic centimeter Metric Units 1 liter (L) = 1000 milliliters (mL) 1 milliliter (mL) = 1 cm3 (or cc) = 1 gram* Which is larger? Click the image to watch a short video about volume. A. 1 liter or 1500 milliliters B. 200 milliliters or 1.2 liters C. 12 cm3 or 1.2 milliliters* * When referring to water Liter Image:

Click the image to watch a short video about volume.
Metric Units kL cL mL L Volume is the amount of space an object takes up. The base unit of volume in the metric system in the liter and is represented by L or l. Standard: 1 liter is equal to one cubic decimeter Metric Units 1 liter (L) = 1000 milliliters (mL) 1 milliliter (mL) = 1 cm3 (or cc) = 1 gram* Which is larger? Click the image to watch a short video about volume. A. 1 liter or 1500 milliliters B. 200 milliliters or 1.2 liters C. 12 cm3 or 1.2 milliliters* * When referring to water Liter Image:

Measuring Volume We will be using graduated cylinders to find the volume of liquids and other objects. Read the measurement based on the bottom of the meniscus or curve. When using a real cylinder, make sure you are eye-level with the level of the water. What is the volume of water in the cylinder? _____mL What causes the meniscus? A concave meniscus occurs when the molecules of the liquid attract those of the container. The glass attracts the water on the sides. Top Image: Bottom Image:

Measuring Liquid Volume
What is the volume of water in each cylinder? Images created at A B C Pay attention to the scales for each cylinder.

Measuring Solid Volume
10 cm 9 cm 8 cm We can measure the volume of regular object using the formula length x width x height. _____ X _____ X _____ = _____ We can measure the volume of irregular object using water displacement. Amount of H2O with object = ______ About of H2O without object = ______ Difference = Volume = ______ Click here for an online activity about volume. Choose Lessons  Volume & Displacement

1 liter (1 L) 1 liter of coke

1 liter (1 L)

Capacity of an eyedropper
1 milliliter (1 mL or 1 ml) Capacity of an eyedropper

1 kiloliter (1kL or 1 kl) About the capacity of 4 bathtubs

Volume Quick Lab

Temperature: Base unit in the metric system is the Celsius.
The degree of hotness or coldness of something Base unit in the metric system is the Celsius.

Temperature A measure of how hot or how cold an object is.
SI unit: Celsius or Centigrade (old term) SI Unit: the kelvin ( K ) Note: not a degree Absolute Zero= 0 K

degree Celsius (°C)

Convert Temperatures Formulas °C x 9/5 + 32 = °F or °C = (°F -32)/1.8
(°F - 32) x 5/9 = °C °F = (°C x 1.8) + 32

Fahrenheit Formula 180°F = 9°F = 1.8°F 100°C 5°C 1°C
Zero point: °C = 32°F °F = 9/5 T°C or °F = 1.8 T°C

Celsius Formula Rearrange to find T°C °F = 1.8 T°C + 32
°F = T°C 1.8

Temperature Conversions
A person with hypothermia has a body temperature of 29.1°C. What is the body temperature in °F? °F = (29.1°C) exact tenth's exact = = 84.4°F tenth’s

Learning Check Pizza is baked at 455°F. What is that in °C? 1) 437 °C

Solution Pizza is baked at 455°F. What is that in °C? 2) 235°C
1.8

Learning Check 1) 19 °F 2) 59°F 3) 5°F
On a cold winter day, the temperature falls to -15°C. What is that temperature in °F? 1) 19 °F 2) 59°F 3) 5°F

Solution 3) 5°F Solution: °F = 1.8(-15°C) + 32 = = 5°F

A long time ago in a faraway galaxy
a king lived in a deluxe castle with all of the neat castle things in it, like a galactic bear rug, and a galactic ping pong table; and the King loved chocolate milk He drank it all day and night long

The Story of King Henry

A long time ago in a faraway galaxy and in a deluxe castle, there lived a monarch who loved chocolate milk. His name was Henry, and he was known to all of his subjects as, King Henry

Throughout his kingdom, King Henry made sure that all of the cows were fed great supplies of chocolate to continue to provide him with his beloved chocolate milk drink. He had very happy cows!

King Henry drank chocolate milk with his breakfast, lunch, and dinner
King Henry drank chocolate milk with his breakfast, lunch, and dinner. He even drank chocolate milk for his bedtime snack. King Henry drank chocolate milk by the liter!

King Henry wanted all living creatures in his kingdom to enjoy chocolate milk as much as he enjoyed chocolate milk. However, a liter was not the best serving size for every creature. The Royal Potter was called for and the command was given for new serving vessels to be created to fit every creature in the kingdom.

For the creatures smaller than the king, the Royal Potter designed
deciliters that were 1/10th the size of a liter, centiliters that were 1/100th the size of a liter, and milliliters that were 1/1000th the size of a liter. The milliliters were just right for the Royal Chocolate Beetles found in the kingdom.

For the creatures greater than the king, the Royal Potter designed,
Dekaliters that were 10 times the size of a liter, Hectoliters that were 100 times the size of a liter, and Kiloliters that were 1000 times the size of a liter. The kiloliters were just right for the Royal Elephants of the kingdom.

The Royal Potter lined the vessels up in his workroom from largest to smallest to show the king.
The king’s vessel was in the center of the line, for the king was the center of the kingdom. The vessels were arranged in the following order: kiloliter hectoliter dekaliter Liter deciliter centiliter milliliter

King Henry loved the new vessels that were designed larger and smaller than his own for all of the living creatures in his kingdom. The Royal Potter explained that the sizes of the original unit of measurement increased and decreased from the king’s liter by multiples of ten. He explained how to convert between the sizes by multiplying by ten or dividing by ten. King Henry wondered how he would ever remember the order of the vessels.

The Royal Potter said that he remembered them by thinking of a saying
The Royal Potter said that he remembered them by thinking of a saying. He said, “I remember the order by saying ‘King Henry Does Usually Drink Chocolate Milk’ and then I have no problem remembering the order.” “That is exactly right!” said King Henry. “Now I shall remember the sizes of the vessels!” He took another big drink of chocolate milk and …

Now it is known as the Metric Conversion Mnemonic
King (kilo, 1,000 units) Henry (hecto, 100 units) Died (deka, 10 units) Unexpectedly (Unit (liter, meter, gram, Celsius) Drinking (deci 1/10 of a unit) Chocolate (centi 1/100 of a unit) Milk (milli, 1/1,000 of a unit)

(K)ing (H)enry (D)ied (W)hile (D)rinking (C)hocolate (M)ilk

(K)ing (H)ector (D)ied (W)hile (D)rinking (C)hocolate (M)ilk
Copyright © 2010 Ryan P. Murphy Copyright © 2010 Ryan P. Murphy

(K)ing (H)ector (D)ied (W)hile (D)rinking (C)hocolate (M)ilk

(K)ing (H)ector (D)ied (U)nexpectedlyhile (D)rinking (C)hocolate
(M)ilk Copyright © 2010 Ryan P. Murphy

Chocolate - Centimeter Milk - Millimeter
King - Kilometer Hector - Hectometer Died - Decameter Unexpectedly Drinking - Decimeter Chocolate - Centimeter Milk - Millimeter Copyright © 2010 Ryan P. Murphy

Unexpectedly Unit (gram, Liter, meter) Drinking - Decimeter
King - Kilometer Hector - Hectometer Died - Decameter Unexpectedly Unit (gram, Liter, meter) Drinking - Decimeter Chocolate - Centimeter Milk - Millimeter Copyright © 2010 Ryan P. Murphy

Chocolate - Centimeter .01m Milk - Millimeter .001m
King Kilometer 1000m Hector - Hectometer 100m Died - Decameter 10m Unexpectedly Unit 1m Drinking - Decimeter .1m Chocolate - Centimeter .01m Milk - Millimeter .001m Copyright © 2010 Ryan P. Murphy

King Kilometer 1000m Hector - Hectometer 100m Died - Decameter 10m Unexpectedly Unit 1m Drinking - Decimeter .1m Chocolate - Centimeter .01m Milk - Millimeter .001m Copyright © 2010 Ryan P. Murphy Copyright © 2010 Ryan P. Murphy

Drinking - Decimeter .1m 10-1 Chocolate - Centimeter .01m 10-2
King Kilometer 1000m 103 Hector - Hectometer 100m 102 Died - Decameter 10m 101 Unexpectedly Unit 1m Drinking - Decimeter .1m Chocolate - Centimeter .01m 10-2 Milk - Millimeter .001m 10-3 Copyright © 2010 Ryan P. Murphy Copyright © 2010 Ryan P. Murphy Copyright © 2010 Ryan P. Murphy

King Kilometer 1000m 103 Hector - Hectometer 100m 102 Died - Decameter 10m 101 Unexpectedly Unit 1m Drinking - Decimeter .1m Chocolate - Centimeter .01m 10-2 Milk - Millimeter .001m 10-3 Copyright © 2010 Ryan P. Murphy

King Kilometer 1000m 103 Hector- Hectometer 100m 102 Died - Decameter 10m 101 Unexpectedly - Unit 1m 100 Drinking - Decimeter .1m Chocolate - Centimeter .01m 10-2 Milk - Millimeter .001m 10-3 Copyright © 2010 Ryan P. Murphy

King Kilometer 1000m 103 Hector- Hectometer 100m 102 Died - Decameter 10m 101 Unexpectedly Unit 1m 100 Drinking - Decimeter .1m Chocolate - Centimeter .01m 10-2 Milk - Millimeter .001m 10-3 Copyright © 2010 Ryan P. Murphy

The Metric System : A measurement system based on the powers of ten.

The simplicity of the metric system stems from the fact that there is only one unit of measurement (or base unit) for each type of quantity measured (length, mass, etc.). Copyright © 2010 Ryan P. Murphy

“I am 1828.80 mm tall.” “I am 182.80 cm tall.”
“I am meters tall.” “I am km tall.” Copyright © 2010 Ryan P. Murphy

You can measure the very small and the very large with the same unit
You can measure the very small and the very large with the same unit. (Meter) Copyright © 2010 Ryan P. Murphy

How many millimeters are in 5.3 meters?
5.3 meters  mm

5.3 meter  mm

5.3 meter  mm 5.3 x 1000 =

5.3 meter  mm 5.3 x 1000 =5300mm

How many kilometers are in 5.3 meters?

5.3 meter  km

5.3 meter  km 5.3 / 1000 =.0053km

How many centimeters are in 1.29 meters?
1.29 meter  cm

1.29 meter  cm 1.29 X 100 =

1.29 meter  cm 1.29 X 100 = 129cm

How many Hectometers are in 4.4 meters?

How many Decimeters are in 14.9 meters?

How many Decimeters are in 14.9 meters?
14.9 x 10 = 149 d

How many Meters are in 6.1 Kilometers?

6.1 km x 1000 =

6.1 km x 1000 = 6.1 x 1000 = 6100

King Henry’s Ladder Make a Metric Ladder in your notebook.

“Use it and you will never get lost!”
Metric Ladder “Use it and you will never get lost!” Kilo Hecto Deka UNITS Gram Liter Meter deci centi milli UNITS 1000 100 10 0.1 0.01 0.001 Unexpectedly - Unit 1m 100 How To Use Your Ladder Start at the unit/prefix given to you (starting point). Count the number of steps/places to the unit/prefix you want (final destination). Move the decimal point the number of steps/places in the same direction.

How many jumps does it take?
Ladder Method 1 2 3 KILO 1000 Units HECTO 100 Units DEKA 10 Units DECI 0.1 Unit Meters Liters Grams CENTI 0.01 Unit MILLI Unit How do you use the “ladder” method? 1st – Determine your starting point. 2nd – Count the “jumps” to your ending point. 3rd – Move the decimal the same number of jumps in the same direction and add zeros for each jump 4 km = _________ m Starting Point Ending Point How many jumps does it take? 1 __. 2 __. 3 __. 4. = 4000 m

Multiplying/Dividing

6 places to the right of the decimal point
Practice Problem 1 How many mg are in 3.6 Kg? grams 3.6 kg 36.0 hectogram milligrams dekagrams decigrams centigrams Gram Kilo Hecto Deka deci centi milli Starting point Final Destination 3,600,000 mg 6 places to the right of the decimal point

5 places to the left of the decimal point
Practice Problem 2 How many hm are in mm? Meter Kilo Hecto Deka deci centi milli Final Destination Starting point hm 5 places to the left of the decimal point

Helpful Mnemonic Try to create your own mnemonic to help you
King Henry Died Usually drinking chocolate milk Kay Hollered Dog ARF! dog can’t move Gram Liter Meter UNITS 1000 100 10 0.1 0.01 0.001 Try to create your own mnemonic to help you remember the prefixes and their order. This will be important because you will not receive the metric map on your quiz.

Please convert 12.36 kg to centigrams
King Kilogram 1000m 103 Hector - Hectogram 100m 102 Died - Decagram 10m 101 While - Standard/Base 1m 100 Drinking - Decigram .1m Chocolate - Centigram .01m 10-2 Milk - Milligram .001m 10-3 Copyright © 2010 Ryan P. Murphy

12345 Please convert 12.36 kg to centigrams 12.36
King Kilograms 1000m 103 Hector - Hectograms 100m 102 Died - Decagrams 10m 101 While - Standard 1m 100 Drinking - Decigrams .1m Chocolate - Centigrams .01m 10-2 Milk - Milligrams .001m 10-3 12345 Copyright © 2010 Ryan P. Murphy

12.36 12345 Please convert 12.36 kg to centigrams 5

1236000.cm 12345 Please convert 12.36 kg to centigrams

1,236,000.cm 12345 Please convert 12.36 kg to centigrams

Please convert 450 mm to hectometers
King Kilometer 1000m 103 Hector - Hectometer 100m 102 Died - Decameter 10m 101 While - Standard 1m 100 Drinking - Decimeter .1m Chocolate - Centimeter .01m 10-2 Milk - Millimeter .001m 10-3 Copyright © 2010 Ryan P. Murphy

Please convert 450 mm to hectometers
King Kilometer 1000m 103 Hector - Hectometer 100m 102 Died - Decameter 10m 101 While - Standard 1m 100 Drinking - Decimeter .1m Chocolate - Centimeter .01m 10-2 Milk - Millimeter .001m 10-3 5 Copyright © 2010 Ryan P. Murphy

Please convert 450 mm to hectometers .000450.0

Please convert 450 mm to hectometers .00450

Please convert 450 mm to hectometers .00450 hm

Please convert 43 cm to Decameters

Please convert 43 cm to Decameters 43.0

Please convert 43 cm to Decameters .043

Please convert 43 cm to Decameters .043 Dm

Please convert 5241 hm to mm 00000. King Kilometer 1000m 103 Hector - Hectometer 100m 102 Died - Decameter 10m 101 While - Standard 1m 100 Drinking - Decimeter .1m Chocolate - Centimeter .01m 10-2 Milk - Millimeter .001m 10-3 Copyright © 2010 Ryan P. Murphy

. Please convert 5241 hm to mm King - Kilometer 1000m 103
Hector - Hectometer 100m 102 Died - Decameter 10m 101 While - Standard 1m 100 Drinking - Decimeter .1m Chocolate - Centimeter .01m 10-2 Milk - Millimeter .001m 10-3 Copyright © 2010 Ryan P. Murphy

. Please convert 5241 hm to mm King - Kilometer 1000m 103
Hector - Hectometer 100m 102 Died - Decameter 10m 101 While - Standard 1m 100 Drinking - Decimeter .1m Chocolate - Centimeter .01m 10-2 Milk - Millimeter .001m 10-3 5 Copyright © 2010 Ryan P. Murphy

Please convert 5241 hm to mm 5 King Kilometer 1000m 103 Hector - Hectometer 100m 102 Died - Decameter 10m 101 While - Standard 1m 100 Drinking - Decimeter .1m Chocolate - Centimeter .01m 10-2 Milk - Millimeter .001m 10-3 5 Copyright © 2010 Ryan P. Murphy

Please convert 5241 hm to mm mm 5 King Kilometer 1000m 103 Hector - Hectometer 100m 102 Died - Decameter 10m 101 While - Standard 1m 100 Drinking - Decimeter .1m Chocolate - Centimeter .01m 10-2 Milk - Millimeter .001m 10-3 5 Copyright © 2010 Ryan P. Murphy

Please convert 5241 hm to mm 524,100,000. mm 5 King Kilometer 1000m 103 Hector - Hectometer 100m 102 Died - Decameter 10m 101 While - Standard 1m 100 Drinking - Decimeter .1m Chocolate - Centimeter .01m 10-2 Milk - Millimeter .001m 10-3 5 Copyright © 2010 Ryan P. Murphy

Please convert 9.9 m to cm cm King Kilometer 1000m 103 Hector - Hectometer 100m 102 Died - Decameter 10m 101 While - Standard 1m 100 Drinking - Decimeter .1m Chocolate - Centimeter .01m 10-2 Milk - Millimeter .001m 10-3 Copyright © 2010 Ryan P. Murphy

Please convert 9.9 m to cm Answer: 990 cm King Kilometer 1000m 103 Hector - Hectometer 100m 102 Died - Decameter 10m 101 While - Standard 1m 100 Drinking - Decimeter .1m Chocolate - Centimeter .01m 10-2 Milk - Millimeter .001m 10-3 Copyright © 2010 Ryan P. Murphy

Please convert 1351 decimeters to cm

Please convert 1351 decimeters to cm Answer: 13,510 cm

Please convert 12 mm to km King Kilometer 1000m 103 Hector - Hectometer 100m 102 Died - Decameter 10m 101 While - Standard 1m 100 Drinking - Decimeter .1m Chocolate - Centimeter .01m 10-2 Milk - Millimeter .001m 10-3 Copyright © 2010 Ryan P. Murphy

Please convert 12 mm to km Answer: km King Kilometer 1000m 103 Hector - Hectometer 100m 102 Died - Decameter 10m 101 While - Standard 1m 100 Drinking - Decimeter .1m Chocolate - Centimeter .01m 10-2 Milk - Millimeter .001m 10-3 Copyright © 2010 Ryan P. Murphy

Please convert 5 m to decimeters

Please convert 5 m to decimeters Answer: 50

Please convert 1.3 x 104 m to centimeters

Limits of Measurement Accuracy and Precision

Accuracy - a measure of how close a measurement is to the true value of the quantity being measured.

Example: Accuracy Who is more accurate when measuring a book that has a true length of 17.0cm? Susan: 17.0cm, 16.0cm, 18.0cm, 15.0cm Amy: 15.5cm, 15.0cm, 15.2cm, 15.3cm

Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is.

Example: Precision Who is more precise when measuring the same 17.0cm book? Susan: 17.0cm, 16.0cm, 18.0cm, 15.0cm Amy: 15.5cm, 15.0cm, 15.2cm, 15.3cm

Example: Evaluate whether the following are precise, accurate or both.
Not Precise Not Accurate Precise Accurate Precise

Introduction to Significant Figures &
Scientific Notation

When taking measurements, the number of digits recorded depends on the precision of the instrument used to measure. The last digit is always an estimate and therefore is called the uncertain or estimated digit. 2. The digits that precede (come before) the last digit are considered the exact or certain digits. 3. The certain/exact digits and the one uncertain, or estimated digit, are called the significant digits.

Significant Figures Scientist use _______________ to determine how _______________ a measurement is. Significant digits in a measurement include all of the _______________ plus one _______________ .

Significant Figures Scientist use significant figures to determine how accurate a measurement is. Significant digits in a measurement include all of the exact/certain digits plus one estimated/uncertain digit.

Definition of a Significant Digit or Figure
The # of digits needed to accurately express a measurement, the 1st non-zero number.

Rules for Significant figures Rule #1
All non zero digits are ALWAYS significant How many significant digits are in the following numbers? _____________ 274 25.632 8.987

Rules for Significant figures Rule #1
All non zero digits are ALWAYS significant How many significant digits are in the following numbers? 274 25.632 8.987

Rule #2 All zeros between significant digits are ALWAYS significant (imbedded) How many significant digits are in the following numbers? 504 60002 9.077 _____________

Rule #2 All zeros between significant digits are ALWAYS significant (imbedded) How many significant digits are in the following numbers? 504 60002 9.077

Rule #3 All FINAL zeros to the right of the decimal ARE significant AND at the end of a number are significant. How many significant digits are in the following numbers? 32.0 19.000 0.0004 _____________

Rule #3 All FINAL zeros to the right of the decimal AND at the end of a number are significant ARE significant. How many significant digits are in the following numbers? 32.0 19.000 0.0004

Rule #4 All zeros that act as place holders are NOT significant (leading zeros) Another way to say this is: zeros are only significant if they are between significant digits OR are the very final thing at the end of a decimal

Rule #4 How many significant digits are in the following numbers
__________ __________ __________ __________

Rule #4 How many significant digits are in the following numbers
0.052 0.0025 Show Khan video on significant digits.

For example… Look at the ruler below
What would be the measurement in the correct number of sig figs?

For example… Look at the ruler below
What would be the measurement in the correct number of sig figs? 13.4 cm13.4 cm

Let’s try this one Look at the ruler below
What would be the measurement in the correct number of sig figs? _______________

Let’s try graduated cylinders
Look at the graduated cylinder below What would be the measurement in the correct number of sig figs? _______________

One more graduated cylinder
Look at the cylinder below… What would be the measurement in the correct number of sig figs? _______________

For example _____________ 0.0002 6.02 x 1023 100.000 150000 800.
How many significant digits are in the following numbers? _____________ 0.0002 6.02 x 1023 150000 800. 7.90 x 10-3

Rules Rounding Significant Digits Rule #1
If the digit to the immediate right of the last significant digit is less that 5, do not round up the last significant digit. For example, let’s say you have the number and you want 3 significant digits

Rounding Rule #2 If the digit to the immediate right of the last significant digit is greater than or equal to 5, you round up the last significant figure Let’s say you have the number and you want 4 significant digits

Let’s try these examples rounded to 3 SF…
200.99 18.22 135.50 98.59 _____________

How wide is our universe?
210,000,000,000,000,000,000,000 miles (22 zeros) This number is written in standard notation. When numbers get this large, it is easier to write them in scientific notation.

A number is expressed in scientific notation when it is in the form
a x 10n where a is between 1 and 10 and n is an integer

Scientific Notation Scientific notation is used to express very _____________ or very _____________ numbers I consists of a number between _____________ followed by _____________ to an _____________ The _____________ can be determined by the number of _____________ you have to move to get only 1 number in front of the decimal

Write the width of the universe in scientific notation.
210,000,000,000,000,000,000,000 miles Where is the decimal point now? After the last zero. Where would you put the decimal to make this number be between 1 and 10? Between the 2 and the 1

2.10,000,000,000,000,000,000,000. How many decimal places did you move the decimal? 23 When the original number is more than 1, the exponent is positive. The answer in scientific notation is 2.1 x 1023

1) Express 0.0000000902 in scientific notation.
Where would the decimal go to make the number be between 1 and 10? 9.02 The decimal was moved how many places? 8 When the original number is less than 1, the exponent is negative. 9.02 x 10-8

Write 28750.9 in scientific notation.
x 10-5 x 10-4 x 104 x 105

Scientific Notation Examples
Place the following numbers in scientific notation: 99.343 4000.1 0.0234 _____________

2) Express 1.8 x 10-4 in decimal notation.
3) Express 4.58 x 106 in decimal notation. 4,580,000

6) Use a calculator to evaluate (0. 0042)(330,000)
6) Use a calculator to evaluate (0.0042)(330,000). On the calculator, the answer is 1386. The answer in standard notation is 1386 The answer in scientific notation is 1.386 x 103

7) Use a calculator to evaluate (3,600,000,000)(23)
7) Use a calculator to evaluate (3,600,000,000)(23). On the calculator, the answer is: 8.28 E +10 The answer in scientific notation is 8.28 x 10 10 The answer in standard notation is 82,800,000,000

Write in PROPER scientific notation
Write in PROPER scientific notation. (Notice the number is not between 1 and 10) 8) x 109 2.346 x 1011 9) x 104 6.42 x 10 2

Write 531.42 x 105 in scientific notation.

Going from Scientific Notation to Standard Notation
You start with the number and move the decimal the same number of spaces as the _____________ . If the exponent is _____________ , the number will be greater than 1 If the exponent is _____________ , the number will be less than 1

Going to Standard Notation Examples
Place the following numbers in Standard notation: _____________ 3 x 106 6.26x 109 5 x 10-4 8.45 x 10-7 2.25 x 103

How to Use Scientific Notation (Exponent Rules)
When adding or subtracting scientific notation #’s, convert the # into the same power of ten (exponent) Practice 4.125 x x10-4 8.97 x104 – 2.62 x103

When adding or subtracting scientific notation #’s, convert the # into the same power of ten (exponent) Practice 4.125 x x10-4 = 4.2 x10-2 8.97 x104 – 2.62 x103 = x104

When multiplying scientific notation #’s, add the exponents together. Think when you multiply, you get more = adding Practice (2.6 x105) (9.2 x10-13) (3.4 x106) (4.2 x10-3)

When multiplying scientific notation #’s, add the exponents together. Think when you multiply, you get more = adding Practice (2.6 x105) (9.2 x10-13) = x10-7 (3.4 x106) (4.2 x10-3) = x10-2

When dividing scientific notation #’s, subtract the exponents together. Think when you divide something, you get less= subtracting. Practice (1.247 x10-3) / (2.9 x10-2) (3.2 x103) / (5.7 x10-2)

When dividing scientific notation #’s, subtract the exponents together. Think when you divide something, you get less= subtracting. Practice (1.247 x10-3) / (2.9 x10-2) = 4.3 x10-2 (3.2 x103) / (5.7 x10-2) = 5.6 x104

Basic SI Measurement Units
Quantity Unit Symbol Length meter m Mass kilogram kg Volume Liter L Temperature Celsius / Kelvin C / K Time second s

Other Measurement SI Units (examples)
Quantity unit Symbol Density kilograms (mass) per cubic meter (volume) kg/m3 Speed meter (length) per second (time) m/s Newton Kg (mass) m/s2 (acceleration) N Energy/Work Joule (kg m2/s2) J

SI Unit Prefixes for Length
Name Symbol Analogy Terrameter Tm 1012 Gigameter Gm 109 Megameter Mm 106 kilometer km 103 decimeter dm 10-1 centimeter cm 10-2 millimeter mm 10-3 micrometer μm 10-6 nanometer nm 10-9

Metric System of Measurement

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