2.1 - SCIENTIFIC NOTATION

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

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

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

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

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

2.2-2.3 - MEASUREMENTS AND

UNITS

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

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

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

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.

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

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)

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