numbers that are extremely large can be difficult to deal with…sooo scientists convert these...
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2.1 - SCIENTIFIC NOTATION
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Scientific Notation
Numbers that are extremely large can be difficult to deal with…sooo
Scientists convert these numbers into scientific notation
Scientific notation expresses numbers as a multiple of two factors:
1. A number between 1 and 10 (only 1 digit to the left of the decimal!)
2. Ten raised to a power
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For example:A proton’s mass
=0.0000000000000000000000000017262 kg
If you put it in scientific notation, the mass of a proton is expressed as 1.7262 x 10-27
kg
Remember:When numbers larger than 1 are expressed
in scientific notation, the power of ten is positive
When numbers smaller than 1 are expressed in scientific notation, the power of ten is negative
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Try these:
Convert 1,392,000 to scientific notation. = 1.392 x 106
Convert 0.000,000,028 to scientific notation.
= 2.8 x 10-8
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Adding and Subtracting using Scientific Notation
• Make sure the exponents are the same!! 7.35 x 102 + 2.43 x 102 = 9.78 x 102
• If the exponents are not the same, you have to make them the same!!
• Tip: if you increase the exponent, you decrease the decimal ----- if you decrease the exponent, you increase the decimal
• Example:Tokyo pop: 2.70 x 107
Mexico City pop: 15.6 x 106 = 1.56 x 107
Sao Paolo pop: 0.165 x 108 = 1.65 x 107
NOW you can add them together and carry thru the exponent
Total= 5.91 x 107
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Multiplying and Dividing using Scientific Notation
Multiplication: Multiply decimals and ADD exponents
Ex : (1.2 x 106) x (3.0 x 104) = 3.6 x 1010 6 + 4 = 10
* Ex: (1.2 x 106) x (3.0 x 10-4) = 3.6 x 102 6 + (-4) = 2
Division: Divide decimals and SUBTRACT exponents
Ex: (5.0 x 108) ÷ (2.5 x 104) = 2.0 x 104 8 – 4 = 4
*Ex: (5.0 x 108) ÷ (2.5 x 10-4) = 2.0 x 1012 8 – (-4) = 12
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2.2-2.3 - MEASUREMENTS AND
UNITS
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Units of Measure SI units: Systeme Internationale d’ Unites standard units of measurement to be understood by all
scientists
Base Units: defined unit of measurement that is based on an object or event in the physical world
there are 7 base units some familiar quantities are time, length, mass, and temp
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Time second (s) Many chemical reactions
take place in less than a second so scientist often add prefixes, based on multiples of ten, to the base units.
ex. Millisecond
Length meter (m) A meter is the distance
that light travels though a vacuum in 1/299 792 458 of a second.
What is a vacuum? Close in length to a yard. Prefixes also apply…ex.
millimeter
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Mass mass is a measurement of
matter kilogram (kg) about 2.2 pounds Masses measured in most
laboratories are much smaller than a kilogram, so scientists use grams (g) or milligrams (mg).
How many grams are in a kilogram? 1000
How many milligrams are in a gram? 1000
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Derived Units
Not all quantities are measured in base units
A unit that is defined by a combination of base units is called a derived unit.
Volume and Density are measured in derived units.
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Volume The space
occupied by an object
Unit = cm3 = mL Liters are used to
measure the amount of liquid in a container (about the same volume as a quart)
Prefixes also applied…ex. milliliter
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Modified Table 2.1 – The Base Units
Quantity Base Unit
Time Second (s)
Length Meter (m)
Mass Kilogram (kg)
Temperature Kelvin (K)
Amount of a substance Mole (mol)
Electric current Ampere (A)
Luminous intensity Candela (cd)
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Modified Table 2.2 – SI Prefixes
Prefix Symbol Numerical Value in Base Units
Power of 10 Equivalent
Giga G 1,000,000,000 109
Mega M 1,000,000 106
Kilo K 1000 103
-- -- 1 100
Deci d 0.1 10-1
Centi c 0.01 10-2
Milli m 0.001 10-3
Micro µ 0.000001 10-6
Nano n 0.000000001 10-9
Pico p 0.000000000001
10-12