Scientific Notation and ErrorScientific Notation and Error

In science, we deal with some In science, we deal with some very very LARGELARGE numbers: numbers:

1 mole = 6020000000000000000000001 mole = 602000000000000000000000

In science, we deal with some In science, we deal with some very very SMALLSMALL numbers: numbers:

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

Scientific NotationScientific 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 kg 91 kg x 602000000000000000000000x 602000000000000000000000

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

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

M x 10M x 10n n

MM is a number between is a number between 11 and and 10 10 nn is an integer is an integer

2 500 000 000

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

.

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

123456789

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

2.5 x 102.5 x 1099

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

0.00005790.0000579

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

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 CALCULATIONCALCULATION

S IN S IN SCIENTIFIC SCIENTIFIC NOTATIONNOTATION

Multiplication and DivisionMultiplication and Division

4 x 104 x 1066

x 3 x 10x 3 x 1066Multiply the front Multiply the front numbers then add numbers then add the exponentsthe exponents1212 x 10x 101212

1.21.2 x 10x 101313Move the decimal Move the decimal behind the first behind the first numbernumber

1.2 x 101.2 x 1099

3 x 103 x 1044

Divide the front Divide the front numbers then numbers then subtract the subtract the exponentsexponents0.40.4 x 10x 1055

44 x 10x 1044Move the decimal Move the decimal behind the first behind the first numbernumber