measurements measurements make observations meaningful

MeasurementsMeasurements make

observations meaningful

International System of Units (SI Units)

• Uses the metric system– Based on units of 10

SI Units

Quantity SI Unit SymbolLength Meter m

Mass Gram g

Time Second s

Temperature Kelvin K

Volume Cubic meter m3

Amount mole mol

Mass• Mass and

weight are NOT the same thing • Weight is

dependant upon gravity, mass is not

Temperature• Kelvin is the SI unit, but

Celsius (C) is often used• K = C + 273Practice:

1. Convert 25oC to K. 2. Convert 352K to oC. 3. Convert -15oC to K.

• Heat and temperature are not the same thing

– Heat is a type of energy– Temperature is a

measurement of energy

Important Temperatures

• Freezing Points for water0oC = 273K = 32oF

• Boiling Points for water100oC = 373K = 212oF

• Absolute zero0 K (-273oC)Theoretically, all movement stops at this

temperature

Volume

• Cubic meter (m3) is the SI unit, but liter (or milliliter) is often used

• Useful Information: – Cubic centimeter (cm3 or cc) =

milliliter (mL)– 1cc = 1mL

Moles• Used to measure the amount (quantity)

of something– 1 mole = 6.02 x 1023 particles

Density

• How much “stuff” in a given area• Density of water (at 250C) = 1.00g/mL• D = m/v

Density Practice

1. A rock has a mass of 3.5kg and a volume of 7.0m3. What is the rock’s density?

2. An object’s density is 8.0g/cm3 and its mass is 1.5g. What is the object’s volume?

3. What would the mass be of a 25mL sample of an object with a density of 0.047g/mL?

Base Units of the Metric SystemQuantity Name Symbol

Length Meter m

Mass Gram g

Volume Liter L

Energy Joule J

* Reference Table D

SI PrefixesPrefix Symbol Meaning

Kilo- k 1000

Hecto- h 100

Deka- da 10

Deci- d 0.1 (1/10)

Centi- c 0.01 (1/100)

Milli- m 0.001 (1/1000)

* Reference Table C

Metric System Conversions

• Kangaroos Hop Down Large Green Mountains During Christmas Morning

– As you move left, move the decimal to the left– As you move right, move the decimal to the

right

Convert each measurement

1. 873cm m

2. 0.05L mL

3. 1200kg mg

4. 75dag hg

5. 560dm km

Significant Figures

• Indicate the precision of a number

• Used for measurements

Rules for determining Sig Figs

1. All non-zero numbers are significant

2. Zeros sandwiched between significant figures are always significant.

3. Zeros before the first non-zero number are not significant. These zeros can be thought of as “place holders”

4. Zeros at the end of a number are only significant when they are decimals.

Atlantic – Pacific Rule• If the decimal is Absent

in a measurement, start on the Atlantic side (right side of the number) with the first nonzero digit. All the preceding digits are significant.

• If the decimal is Present in a measurement, start on the Pacific side (left side of the number) with the first nonzero digit. All the following digits are significant.

Atlant

ic

Paci

fic

Sig Fig Practice

1. 803

2. 60.56

3. 5.780

4. 0.0025

5. 0.08150

6. 200.

7. 1.50 x 1021

Exact Numbers• Exact numbers, such as the number of people in

a room, have an infinite number of significant figures. Exact numbers are counting up how many of something are present, they are not measurements made with instruments. Another example of this are defined numbers, such as 1 foot = 12 inches. There are exactly 12 inches in one foot. Therefore, if a number is exact, it DOES NOT affect the accuracy of a calculation nor the precision of the expression. Some more examples:

• There are 100 years in a century.• 2 molecules of hydrogen react with 1 molecule

of oxygen to form 2 molecules of water.

Addition/Subtraction

• Round your final answer to the same number of decimal places as the figure with the least number of decimal places

Practice

1. 2.1 g

12.59 g

+ 34.73 g

2. 109.05 g

- 62.4 g

Multiplication/Division

• Round your final answer to the same number of significant figures as the number with the least number of significant figures

Practice

1. 3.127

x 8.01

2. The mass of a solid is 3.60g and its volume is 1.8cm3. What is the density of the solid?

Scientific Notation

• Used as a shorthand for writing very small or very large numbers

• Always written in the form a x 10b 1 a < 10Exponent will be positive for numbers greater than 1Exponent will be negative for numbers less than 1

Practice

1. 103,000 =

2. 2 x 106 =

3. 0.6842 =

4. 8.56 x 10-4 =

Adding/Subtracting

• Must have the same exponent first! Change the smaller exponent into the larger one

• Add/Subtract the non-exponent• Keep the same exponent

Examples: 1. 2.7x103 + 3.2x102

2. 7.58x1020 – 6.2x1021

Multiplying/Dividing

• Multiply/Divide non-exponent

• Add/Subtract exponentExamples: • (7.2 x 10-2) (3.4 x 104) =

• 7.5 x 106 =

2.5 x 102

Percent Error

Measured – Accepted x 100

Accepted

Example: Methyl alcohol boils at 65oC, a student measures it to be 68oC. What is the percent error?

* Also given on

Reference Table T

Dimensional Analysis

• You can multiply anything by 1 and not change the value of the number

• Multiplying by conversion factors is the same as multiplying by 1

• Just keep track of your units!!!!!

Examples: 1. How many seconds are there in 5.00 days?

2. Calculate the number of minutes in 2.0 years? Express your answer in scientific notation.