Scientific Scientific NotationNotation

In science, we deal with some very LARGE numbers:

1 mole = 6020000000000000000000001 mole = 602000000000000000000000

In science, we deal with some very SMALL numbers:

Mass of an electron =Mass of an electron =0.000000000000000000000000000000091 kg0.000000000000000000000000000000091 kg

Scientific Notation

Imagine the difficulty of Imagine the difficulty of calculating the mass of 1 mole calculating the mass of 1 mole of electrons!of electrons!

0.00000000000000000000000000000000.000000000000000000000000000000091 kg91 kg x 602000000000000000000000x 602000000000000000000000

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Scientific Scientific Notation:Notation:A method of representing very A method of representing very

large or very small numbers in large or very small numbers in the form:the form:

M x 10M x 10nn

MM is a number betweenis a number between 11 andand 99 nn is an integeris an integer

2 500 000 000

Step #1: Step #1: Insert an understood decimal point

.

Step #2: Step #2: Decide where the decimal must end up so that one number is to its leftStep #3: Step #3: Count how many places you bounce the decimal point

123456789

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

2.5 x 102.5 x 1099

The exponent is the number of places we moved the decimal.

0.00005790.0000579

Step #2: Step #2: Decide where the decimal must end up so that one number is to its leftStep #3: Step #3: Count how many places you bounce the decimal pointStep #4: Step #4: Re-write in the form M x 10n

1 2 3 4 5

5.79 x 105.79 x 10-5-5

The exponent is negative because the number we started with was less than 1.

PERFORMING PERFORMING CALCULATIONS CALCULATIONS IN SCIENTIFIC IN SCIENTIFIC

NOTATIONNOTATION

ADDITION AND ADDITION AND SUBTRACTIONSUBTRACTION

4 x 104 x 1066

+ 3 x 10+ 3 x 1066

IFIF the exponents the exponents are the same, we are the same, we simply add or simply add or subtract the subtract the numbers in front numbers in front and bring the and bring the exponent down exponent down unchanged.unchanged.

77 x 10x 1066

4 x 104 x 1066

- 3 x 10- 3 x 1066

The same holds The same holds true for true for subtraction in subtraction in scientific scientific notation.notation.

11 x 10x 1066

4 x 104 x 1066

+ 3 x 10+ 3 x 1055

If the exponents If the exponents are NOT the are NOT the same, we must same, we must move a decimal to move a decimal to makemake them the them the same.same.

4.00 x 104.00 x 1066

+ + 3.00 x 103.00 x 1055 + + .30 x 10.30 x 1066

4.304.30 x 10x 1066

Move the Move the decimal decimal on the on the smallersmaller number!number!

4.00 x 104.00 x 1066

A Problem for A Problem for you…you…

2.37 x 102.37 x 10-6-6

+ 3.48 x 10+ 3.48 x 10-4-4

2.37 x 102.37 x 10-6-6

++ 3.48 x 103.48 x 10-4-4

Solution…Solution…002.37 x 10002.37 x 10--

66

+ 3.48 x 10+ 3.48 x 10-4-4

Solution…Solution…0.0237 x 100.0237 x 10-4-4

3.5037 x 103.5037 x 10-4-4

Multiplying with Scientific Notation

Add the Exponents

102 X 103 = 105

100 X 1000 = 100,000

Multiplying with Scientific Notation

(4.6 X 104) X (5.5 X 103) = ?

(3.1 X 103) X (4.2 X 105) = ?

Dividing with Scientific Notation

Subtract the Exponents

104/103 = 101

10000X 1000 = 10

Dividing with Scientific Notation

(4.6 X 104) / (5.5 X 103) = ?

(3.1 X 103) / (4.2 X 105) = ?