Transcript Scientific Notation

Scientific Notation
2012-2013
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.

Scientific notation consists of
two parts:
A number is expressed in scientific
notation when it is in the form
a x 10n
where a is between 1 and 10
and n is an integer
Are these numbers in scientific
notation?

2.98393 x 109

4.19385930 x 104/5

9.8920188438 x 10-3

2.22221 x 10000
Yes
No
Yes
No
Powers of Ten
When multiplying or dividing by powers
of ten, we can use a shortcut to solve.
 Multiplying:

1. count the number of zeros
2. move decimal point that number of places
to the right

Dividing:
1. count the number of zeros
2. move decimal point that number of places
to the left
Exponents of Ten

When powers of ten are expressed as
exponents, the exponent represents the
number of zeros.
Ex. 105 = 100,000
 Ex. 1012 = 1,000,000,000,000

Examples

38 x 102= 3,800

2.43 x 107 = 24,300,000

0.00321 x 1,000 = 3.21

12 ÷ 10,000= 1,200,000

93.6 ÷ 102 = 9,360
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 greater than
1, then the exponent is positive.
Example 1
Given: 289,800,000.
 2.898
 Decimal point moved 8 places
 Original number is greater than 1
 Answer: 2.898 x 108

Example 2
Given: 0.000567
 5.67
 Decimal point moved 4 places
 Original number is less than 1
 Answer: 5.67 x 10-4

Convert to Scientific Notation




0.00264
2.64 x 10-3
3,298,034
3.298034 x 106
4
134.62
4 x 100
1.3462 x 102
Changing scientific notation to
standard form.
To change scientific notation to
standard form…
Simply move the decimal point to the
right for positive exponent of 10.
 Move the decimal point to the left for
negative exponent of10.

(Use zeros to fill in places.)
Example 3
Given: 5.093 x 106
 moved 6 places to the right
 Fill in extra places with zeros
 Answer: 5,093,000

Example 4
Given: 1.976 x 10-4
 moved 4 places to the left
 Fill in extra places with zeros
 Answer: 0.0001976

Convert to standard form

3.256 x 10-2
0.03256

5.6023 x 104
56,023

9. 2 x 108
920,000,000
Using the Calculator

In order to enter a number in scientific
notation into the calculator, we use the
EE button
Ex. 3.26 x 104
 enter the number : 3.26
 click the 2nd key
 click the EE (above the x-1)
 enter the exponent : 4
 click equals

Using the Calculator
When a calculation yields a very large
or very small number, some calculators
will give the answer in scientific
notation.
 If the calculator says a EE b

– The a is the number
– The b is the exponent of ten
Ex. 4.3 EE -7 = 4.3 x 10-7