Scientific Notation

Often used to express

very large or

very small numbers.

Also used to maintain

correct number of

significant figures.

Form: (# from 1 to 9.999) x 10exponent

800 = 8 x 10 x 10

= 8 x 102

2531 = 2.531 x 10 x 10 x 10

= 2.531 x 103

0.0014 = 1.4 / 10 / 10 / 10

= 1.4 x 10-3

Change to standard form.

1.87 x 10–5 =

3.7 x 108 =

7.88 x 101 =

2.164 x 10–2 =

370,000,000

0.0000187

78.8

0.02164

000000187000000..

Change to scientific notation.

12,340 =

0.369 =

0.008 =

1,000,000,000 =

1.234 x 104

3.69 x 10–1

8 x 10–3

1 x 109

Using the Exponent Keyon a Calculator

EXP

EE

EE or EXP means “times 10 to the…”

How to type out 6.02 x 1023:

6 EE. 0 32 2

6 y x. 0 32 2

x 16 . 0 2 EE 320

y x 32x 16 . 0 2 0

Don’t do it like this…

…or like this…

…or like this:

How to type out 6.02 x 1023:

6 EE. 0 32 2

WRONG!

WRONG!

TOO MUCH WORK.

Also, know when to hit your (–) sign…

…before the number,

…after the number,

…or either one.

Example: 1.2 x 105 2.8 x 1013

But instead is written…

=

1 . 2 EE 5

32 . 8 EE 1

Type this calculation in like this:

This is NOT written… 4.3–9

4.2857143 –09Calculator gives…

4.2857143 E–09or…

4.3 x 10–9 4.3 E –9or

3-6 10 x 1.23 10 x 4.35

4-6- 10 x 8.7- 10 x 7.5

4-16- 10 x 9.86 10 x 5.76

1111 10 x 3.3 10 x 8.8

= -6.525 x 10-9

= 5.3505 x 103 or 5350.5

= 5.84178499 x 10-13

report -6.5 x 10-9 (2 sig. figs.)

report 5.35 x 103 (3 sig. figs.)

report 5.84 x 10-13 (3 sig. figs.)

= 2.904 x 1023

report 2.9 x 1023 (2 sig. figs.) 8-23 10 x 5.1- 10 x 6.022 = -3.07122 x 1016

report -3.1 x 1016 (2 sig. figs.)

Scientific Notation

• Scientific Notation• Converting Numbers to Scientific Notation• How to Use a Scientific Calculator

Scientific Notation

We often use very small and very large numbers in chemistry.Scientific notation is a method to express these numbers in amanageable fashion.

Thus 0.000 000 1 cm can be written 1 x 10-7 cm.

Lets see why…

Scientific notation expresses a number as the product of twofactors, the first falling between 1 and 10 andthe second being a power of 10.

Method to express really big or small numbers.

Format is Mantissa x Base Power

We just move the decimal point around.

Decimal part of original number

Decimal you moved

6.02 x 1023

602000000000000000000000

Scientific Notation

5000 = 5 x 103 or 5 3

5 x (10 x 10 x 10) 5 x 1000 5000

Numbers > one have a positive exponent.

Numbers < one have a negative exponent.

EE

Numbers are written in the form M x 10n, where the factor M is a number greater than or equal to 1 but less than 10 and n is a whole number.

x 10n

Converting Numbers to Scientific Notation

0 . 0 0 0 0 2 2 0 5

1 2 3 4 5

2.205 x 10-5

In scientific notation, a number is separated into two parts.The first part is a number between 1 and 10.

The second part is a power of ten.

How to Use a Scientific Calculator

How to enter this on a calculator:

5.44 7 8.1 4EE EE

5.44 7 8.1 4EXP =EXP

.

671.6049383

rounded to 6.7 x 102

ENTER

Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 52

.

Divide: (5.44 x 107) (8.1 x 104)..

OR

5.44 000754400000.8.10004671.604938

..

Rule for MultiplicationCalculating with Numbers Written in Scientific Notation

When multiplying numbers in scientific notation, multiply thefirst factors and add the exponents.

Sample Problem: Multiply 3.2 x 10-7 by 2.1 x 105

(3.2) x (2.1) = 6.72

(-7) + (5) = -2 or 10-2

6.72 x 10-2

Exercise: Multiply 14.6 x 107 by 1.5 x 104 2.19 x 1012

Rule for DivisionCalculating with Numbers Written in Scientific Notation

When dividing numbers in scientific notation, divide the first factor in the numerator by the first factor in the denominator.Then subtract the exponent in the denominator from the exponent in the numerator.

Sample Problem: Divide 6.4 x 106 by 1.7 x 102

(6.4) (1.7) = 3.76

(6) - (2) = 4 or 104

3.76 x 104

Exercise: Divide 2.4 x 10-7 by 3.1 x 1014 7.74 x 10-22

.

.

Rule for Addition and SubtractionCalculating with Numbers Written in Scientific Notation

In order to add or subtract numbers written in scientific notation, you must express them with the same power of 10.

Sample Problem: Add 5.8 x 103 and 2.16 x 104

(5.8 x 103) + (21.6 x 103) = 27.4 x 103

Exercise: Add 8.32 x 10-7 and 1.2 x 10-5 1.28 x 10-5

2.74 x 104

Using Scientific Notation for Expressing the Correct Number of Significant Figures

Measurement Number of significant figures it contains

Measurement Number of significant figures it contains

25 g

0.030 kg

1.240560 x 106 mg

6 x 104 sec

246.31 g

20.06 cm

1.050 m

0.12 kg

1240560. cm

6000000 kg

6.00 x 106 kg

409 cm

29.200 cm

0.02500 g

2

2

7

1

5

4

4

2

7

1

3

3

5

4