2.2

Scientific Notation and Significant Figures

In science, we deal with some very LARGE

numbers:

1 mole = 602000000000000000000000

In science, we deal with some very SMALL

numbers:

Mass of an electron =

0.000000000000000000000000000000091 kg

Scientific Notation:

Imagine the difficulty of calculating the mass of

1 mole of electrons!

0.000000000000000000000000000000091 kg

x 602000000000000000000000

???????????????????????????????????

Scientific Notation:

A method of representing very large or very small

numbers in the form:

M x 10n

M is a number between 1 and 10

n is an integer

300,000,000 = 3.0 x 108

.000034 = 3.4 x 10-5

• Only one number should be to the left of the decimal

• This is wrong: 34.0 x 10-4

• This is wrong: .56 x 10-4

• This is correct: 7.2 x 10-4

• If the number goes down, the exponent goes up

• If the number goes up, the exponent goes down

Scientific Notation Rules

2 500 000 000

Step #1: Insert an understood decimal point

.

Step #2: Decide where the decimal must end up so that one

number is to its left

Step #3: Count how many places you bounce the decimal

point (This is equal to n)

1 2 3 4 5 6 7 8 9

Step #4: Re-write in the form M x 10n

2.5 x 109

The exponent is the

number of places we

moved the decimal.

0.0000579

Step #2: Decide where the decimal must end up so that one number

is to its left

Step #3: Count how many places you bounce the decimal point

Step #4: Re-write in the form M x 10n

1 2 3 4 5

Step #1: Insert an understood decimal point (Decimal point is

given in this problem)

5.79 x 10-5

The exponent is negative because

the number we started with was less

than 1.

Example: The Distance From the Sun to the Earth is 93,000,000 miles Step #1: 93,000,000.

Step #2: 93,000,000 = 9.3000000

Write numbers without zeros: 9.3000000 = 9.3

Step 3: Count how many places you moved your decimal and

make that your power of ten. (7 places)

Step 4: 9.3 X 107

Example The Distance From the Sun to the Earth is 93,000,000 miles

93,000,000 - Decimal or Standard Form

9.3 X 107 - Scientific Notion

98,500,000 = 9.85 x 10?

64,100,000,000 = 6.41 x 10?

279,000,000 = 2.79 x 10?

Practice Problems:

9.85 x 107

6.41 x 1010

2.79 x 108

Practice Problems

Convert to scientific notation:

5400000

5.4 x 106

.000045

4.5 x 10-5

Scientific Notation to Standard Form

Move the decimal to the right - The number to the power of 10.

Example:

3.4 x 105 in scientific notation

3.4 = 340000 (Move the decimal right five places)

340,000 in standard form

6.27 x 106

9.01 x 104

4.56 x 10-3

Practice Problems:

6,270,000

90,100

.00456

Significant Figures

The measurable units of a measuring device plus

one estimated digit.

Significant Figures

.Pacific -----------------------Atlantic

Practice Problems

• 34.007

• .0078

• 234000

• 6700.100

• 4000.00

• 1.005

Pie Graph and Table

A pie chart is a circular chart divided into sectors, each

sector shows the relative size of each value.

Bar Graphs

A bar graph is a graph drawn using rectangular bars to

show how large each value is. (The bars can be horizontal

or vertical)

Line Graphs A line graph is a graph that uses points connected by lines to

show how something changes in value (as time goes by, or

as something else happens).