Why is thisstuff important?

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 Key

on a Calculator

EXP

EE2nd

EE or EXP means “times 10 to the…”

How to type out 6.02 x 1023:

6 EE. 0 32 2

How to type out 6.02 x 1023:

6 EE. 0 32 2

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

2nd

2nd

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.)

(–)

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 )x (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 ) X (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 ) + ( 2.16 x 104 )

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

Exercise: Add (8.32 x 10-7 ) + (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