CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 3. Logs and Exponents

3.3 Scientific Notation

Here you will review how to write very large and very small numbers in scientific notation and how to use scientific
notation in arithmetic operations.
In science, measurements are often extremely small or extremely large. It is inefficient to write the many zeroes
in very small numbers like 0.00000000000000523. Usually, the order of magnitude and the first few digits of the
number are what people are interested in. How should you represent these extreme numbers?

Watch This

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/60996

http://www.youtube.com/watch?v=hY-ecKyZ244 James Sousa: Scientific Notation

Guidance

Scientific notation is a means of representing very large and very small numbers in a more efficient way. The general
form of scientific notation isa· 10 b
Theais a number between 1 and 10 and most often includes a decimal. The integerbis called the order of
magnitude and is a measure of the general size of the number. Ifbis negative then the number is small and ifbis
positive then the number is large.

1 , 240 , 000 = 1. 24 · 106

0. 0000354 = 3. 54 · 10 −^5

Note that when switching to and from scientific notation the sign ofbindicates which direction and how many places
to move the decimal point.
Multiplying and dividing numbers that are in scientific notation is just an exercise in exponent rules:

(a· 10 x)·(b· 10 y) =a·b· 10 x+y

(a· 10 x)÷(b· 10 y) =ab· 10 x−y

Addition and subtraction require the numbers to have identical order of magnitudes.

1. 2 · 106 − 5. 5 · 105 = 12 · 105 − 5. 5 · 105 = 6. 5 · 105
   Example A