Metric Conversions, Dimensional Analysis, and

Scientific Notation

International System of Units (SI)• Built on a set of

seven metric units, called base units (base units contain no prefix…examples are grams, meter, and liter)

Prefixes are added to the names of SI base units to represent quantities that are larger or smaller than the base units (examples are kilogram, centimeter, and milliliter)

Official SI Units of Measurement

• Length – meter (m)• Mass – kilogram (kg)• Time – second (s)• Temperature – Kelvin (K)• Amount of substance – mole (mol)• Electric current – ampere (A)• Luminous intensity – candela (cd)

Metric Prefixes and Symbols• Giga —G 1,000,000,000• Mega —M 1,000,000• Kilo –k 1,000• Hecto –h 100• Deca –da 10• BASE• Deci – d 0.1• Centi – c 0.01• Milli – m 0.001• Micro--µ 0.000001 • Nano—n 0.000000001

King Henry Died By Drinking

Chocolate Milk

Bigger than base

Smaller than base

How would you write…

--Millisecond

--Decagram

--Deciliter

--Gram

--Kilometer

--Centigram

Which is larger?

• 1 centimeter or 1 meter?• 1 decagram or 1 gram?• 1 millimeter or 1 centimeter?• 1 kiloliter or 1 liter?• 1 decimeter or 1 hectometer?• 1 gram or 1 milligram? • 1 milliliter or 1 kiloliter?

Hardest part about converting between units…what are the

equivalences?? • This can be easy though! Use your chart to help you! • 1 meter = _________ cm? • Start by thinking…which is larger? 1 meter or 1

centimeter?• Since a meter is larger, we are going to need many

centimeters to equal 1 meter. • So how many centimeters do we need? Use the prefix

“centi” to help you! “Centi-” means “hundreth” so a centimeter is a hundreth (1/100) of a meter.

• Therefore it takes 100 centimeters to equal 1 meter.

100

What are the equivalences?? • 1 kilometer = _________ meters? • Which is larger? 1 kilometer or 1 meter? 1 kilometer• Since a kilometer is larger, we are going to need many

meters to equal 1 kilometer. • So how many meters do we need? Use the prefix

“kilo” to help you! “Kilo-” means “thousand” so a kilometer is a thousand meters.

• Therefore it takes 1000 meters to equal 1 kilometer.

1000

What are the equivalences?? • 1 milligram = _________ gram? • Which is larger? 1 milligram or 1 gram? 1 gram• Since 1 gram is larger, a milligram will only be a

fraction of the gram. • What fraction? Use the prefix “milli” to help you!

“Milli-” means “thousandth” so a milligram is a thousandth (1/1000) of a gram.

• 1/1000 of a gram = 0.001 gram• Therefore, 1 milligram = 0.001 grams

0.001

Practice on your own! Example:

• 1 kiloliter = ______ liters• 1 gram = _______ centigrams • 1 meter = ______ millimeters • 1 decagram = _________ grams • 1 liter = ________ deciliters • 1 milliliter = _______ liters• 1 centigram = ______ grams

1000

1001000

10

100.001

0.01

Derived SI units***Made by combining

multiple single SI units! • Area – square meter (m2)• Volume – cubic meter (m3)• Density – kg per cubic meter (kg/m3)• Molar mass – kg per mole (kg/mol)• Concentration – moles per liter (M)• Molar volume – cubic meters per mol

(m3/mol)

Scary problem?

• (80) x (50) x (1) x (40) x (30) x (2) = ?

(40)(30) (20) (80) (50) (1)

No! Mark out commonalities on the top and the bottom when all numbers are multiplied!

(80) x (50) x (1) x (40) x (30) x (2) = 2 = 1

(40)(30) (20) (80) (50) (1) 20 10

Dimensional Analysis• The technique of converting between

unitsUses:1. Unit equalities – an equation that shows

how different units are related (ex. 1 cm = 0.01 m)

2. Conversion factors – equation that always equals one (ex. 1cm/0.01m)*Multiply the conversion factor so that units you do not want cancel, and the unit that you do want ends up on top.

Example Problems

• A baker uses 1.5 tsp of vanilla extract in each cake. How much vanilla is consumed to make 800 cakes? (1 tsp = 5 mL)

Conversion factor: 1.5 tsp or 1 cake 1 cake 1.5 tsp

Use it!800 cakes x 1.5 tsp = 1200 tsp

1 cake

Answer 1200 tsp

What did we just do? Went from one unit to another…

• Start with writing down the current unit• Use as many conversion factors as

necessary to go from the current units to the desired units

• Make sure the undesired units “cancel out” (by being located on the top and bottom) leaving only the desired unit on the top at the end

Example Problems• A person drinks eight glasses of water a day.

Each glass contains 300 mL. How many mL will a person drink in 1 yr?

• Conversion factors: 8 glasses of water or 1 day 1 day 8 gl. of waterAlso: 1 glass of water or 300 mL 300 mL 1 glass of water

1 year x 365 days x 8 gl. of water x 300 mL = 1 year 1 day 1 gl. of water

Answer 876,000 mL

Practice on your own! Example:

• A roll of copper wire contains 15 m of wire. What is the length of the wire in centimeters? – Start by writing down the current units

15 meters– Use conversion factors to go from current

unit (meters) to desired unit (centimeters)

15 meters x 100 centimeters = 1500 cm

1 meter

Dimensional Analysis

• Convert 18 inches to feet

• Convert 6489 feet to miles – (Note: 1 mile = 5280 feet)

18 inches x 1 foot = 1.5 foot 12 inches

6489 feet x 1 mile = 1.23 miles 5280 feet

Double it Up!

• Convert 32 miles/hour to feet/second.

32 miles x 1 hour x 1 min x 5280 ft = 46.9 ft/sec

1 hour 60 mins 60 sec 1 mile

Scientific Notation

Steps for converting:• Insert a decimal into the original number

to create a new number that is between the value of 1 and 10.

Ex. 123,000,000,000 1.23000000000• To find the exponent, count the number of

places from the decimal to the end of the number.

Ex. In 123,000,000,000 there are 11 places therefore we write it as 1.23 x 1011

• Numbers less than 1 (decimal numbers) will have negative exponents

Ex. 0.000001 will be written as 1 x 10-6

Scientific Notation Practice!

Convert the following: • 12,000 • 456• 7,000,000• 0.0043• 0.09833• 30 • 0.30 • 8