Transcript Scientific_Notation

Scientific Notation
What is Scientific Notation?
Scientific notation is a way of
expressing really big numbers or
really small numbers.
 It is most often used in “scientific”
calculations where the analysis
must be very precise.

Why use scientific notation?
For very large and very small
numbers, these numbers can be
converted into scientific notation to
express them in a more concise
form.
 Numbers expressed in scientific
notation can be used in a
computation with far greater ease.

Scientific notation consists
of two parts:

A number that is 1 or greater but less than
10

Multiplied by a power of 10
Nx
x
10
Are the following in scientific notation??
23.983 93 x 10^9
4.193 859 30 x 104
98 920.188 438 x 10^-3
2.222 21 x 10 000
9.002 x 100
3.999 293 4 x 10^1
0.110 382 749 392 092 028 475 7 x 102
1.00x 10^56
2.394 03 x 10-23
9.000 78 x 10^-1
Are the following in scientific notation??
23.983 93 x 10^9
No
4.193 859 30 x 104
Yes
98 920.188 438 x 10^-3
No
2.222 21 x 10 000
No
9.002 x 100
Yes
3.999 293 4 x 10^1
Yes
0.110 382 749 392 092 028 475 7 x 102
No
1.00x 10^56
Yes
2.394 03 x 10-23
Yes
9.000 78 x 10^-1
Yes
Changing standard form to
scientific notation.
To change standard form to
scientific notation…
Place the decimal point so that there
is one non-zero digit to the left of the
decimal point.
 Count the number of decimal places
the decimal point has “moved” from
the original number. This will be the
exponent on the 10.

Continued…
If the original number was less than 1,
then the exponent is negative. If the
original number was 10 or greater, then
the exponent is positive.
 If the original number was less than 10
(9.999) but 1 or greater (1 or 1.111 11),
then the exponent is zero (0) which means
the number is multiplied by 1.
6 x 100 = 6
(10 to the power of zero equals one)

Example 1
Given: 289 800 000
 Use: 2.898 (moved 8 places)
 Answer: 2.898 x 108

Example 2
Given: 0.000 567
 Use: 5.67 (moved 4 places)
 Answer: 5.67 x 10-4

Change each of the following standard form
numbers into scientific notation.

378 000

0.009 34

0.000 000 983

1.928 4

34.903
Change each of the following standard form
numbers into scientific notation.

378 000

3.78 x 105

0.009 34

9.34 x 10^-3

0.000 000 983

9.83 x 10-7

1.928 4

1.928 4 x 10^0

34.903

3.940 3 x 101
Change each of the following standard form
numbers into scientific notation.

783 920

1 039

0.167

90.382 7

12.34
Change each of the following standard form
numbers into scientific notation.

783 920

7.839 2 x 105

1 039

1.039 x 10^3

1.67 x 10-1

0.167

90.382 7

9.038 27 x 10^1

12.34

1.234 x 101
Change each of the following standard form
numbers into scientific notation.

190

0.001 278 0

0.123

1.00

23 289 472 909
Change each of the following standard form
numbers into scientific notation.

190

1.9 x 102

0.001 278 0

1.278 0 x 10^-3

0.123

1.23 x 10-1

1.00

1 x 100

23 289 472 909

2.328 947 290 9 x 10^10
Changing scientific notation
to standard form.
To change scientific
notation to standard form…
Simply move the decimal point to the
right for positive exponent 10.
 Move the decimal point to the left for
negative exponent 10.
 For 10^0, just drop the 10^0.

(Use zeros to fill in places.)
Example 3
Given: 5.093 x 106
 Answer: 5 093 000 (moved 6 places
to the right)

Example 4
Given: 1.976 x 10-4
 Answer: 0.000 197 6 (moved 4
places to the left)

Change each of the following numbers in
scientific notation into standard form
numbers.
 1.493 x 105

2.908 x 10^-4

3.902 84 x 102

1.333 x 10-1

6.000 000 9 x 10^7
Change each of the following numbers in
scientific notation into standard form
numbers.
 1.493 x 105
 149 300

2.908 x 10^-4

0.000 290 8

3.902 84 x 102

390.284

1.333 x 10-1

0.133 3

6.000 000 9 x 10^7

600 000 09
Change each of the following numbers in
scientific notation into standard form
numbers.
 2.345 x 104

4.56343 x 100

7.904 x 10^-3

3.5093 x 10-6

2.309 x 10-2
Change each of the following numbers in
scientific notation into standard form
numbers.
 2.345 x 104
 23 450

4.56343 x 100

4.563 43

7.904 x 10^-3

0.007 904

3.5093 x 10-6

0.000 003 509 3

2.309 x 10-2

0.023 09
Change each of the following numbers in
scientific notation into standard form
numbers.
 5.9 x 10^3

1.2349 x 10-4

6.66 x 10^1

4.543 x 100

9.9989 x 10^4
Change each of the following numbers in
scientific notation into standard form
numbers.
 5.9 x 10^3
 5 900

1.2349 x 10-4

0.000 123 49

6.66 x 10^1

66.6

4.543 x 100

4.543

9.9989 x 10^4

99 989
Even More Practice

Below is a list of links to games and
activities all having to do with
scientific notation.
– http://www.aaamath.com/dec71idec2sci.html
– http://janus.astro.umd.edu/cgibin/astro/scinote.pl
– http://www.xpmath.com/forums/arcade.
php?do=play&gameid=21#.Ubu80vF1b0