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Scientific Notation and Error. Scientific Notation. 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.

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Scientific notation and error

Scientific Notation

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 and error

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

0.000000000000000000000000000000091 kg

x 602000000000000000000000

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Scientific notation and error

Scientific Notation: electrons!

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


Scientific notation and error

. electrons!

2 500 000 000

9

7

6

5

4

3

2

1

8

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

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


Scientific notation and error

2.5 x 10 electrons!9

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


Scientific notation and error

0.0000579 electrons!

1

2

3

4

5

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


Scientific notation and error

5.79 x 10 electrons!-5

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


Scientific notation and error

PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION electrons!

Multiplication and Division


Scientific notation and error

4 x 10 electrons!6

Multiply the front numbers then add the exponents

x 3 x 106

12

x 1012

Move the decimal behind the first number

1.2

x 1013


Scientific notation and error

Divide the front numbers then subtract the exponents electrons!

1.2 x 109

 3 x 104

0.4

x 105

Move the decimal behind the first number

4

x 104


Percent error
Percent Error electrons!

  • Mathematical measure of accuracy

  • Tells how far a measurement varies from the actual value

Actual Value – Measured Value

X 100

% Error =

Actual Value