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# Scientific Notation and Error - PowerPoint PPT Presentation

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

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

0.000000000000000000000000000000091 kg

x 602000000000000000000000

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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

. 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

2.5 x 10 electrons!9

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

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

5.79 x 10 electrons!-5

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

Multiplication and Division

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

1.2 x 109

 3 x 104

0.4

x 105

Move the decimal behind the first number

4

x 104

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