Scientific Notation and SI Prefixes

Handling the Big and the Small

Powers of Ten• In science we use

powers of ten to handle the vast range of scale in the universe

• Many physical quantities can be very large or very small

Pow

er M

ath Exponent Power of

TenValue Name

-9 10-9 0.000000001 One Billionth-6 10-6 0.000001 One Millionth

-3 10-3 0.001 One Thousandth

-2 10-2 0.01 One Hundredth

-1 10-1 0.1 One Tenth

0 100 1 One

1 101 10 Ten

2 102 100 Hundred

3 103 1000 Thousand

6 106 1,000,000 Million

9 109 1,000,000,000 Billion

Scientific Notation

• Scientific notation is the standard method of handling large and small numbers– SN can handle any number, not just big and small– SN exists for our convenience– SN is neither better nor worse than other forms– We use SN at our discretion for purposes of clarity

and ease of use– When numbers are expressed in SN, the number of

significant figures is explicit and can no longer be ambiguous

Standard Form• The standard form of SN is most often used• The standard form is just a convention to aid

communication (you don’t have to always use it)

1.23 × 1011

1 coefficient 10 base = 10 exponent = any integer

• Examples: 103,000 = 1.03 × 105

0.00022 = 2.2 × 104

coefficient base exponent

Scientific Notation and Calculators• Scientific calculators have a SN function that

makes our lives much easier! Use it!• The button usually says either “EE” or “Exp”• To put in 1.23 × 1011 you type “1.23” then “EE”

then “11” and it will show “1.23E+11”• It will give answers in the same form:

“5.76E-6” means “5.76 × 106”• Once you have entered a SN value in this way,

the calculator treats it as one inseparable number

SI Prefixes• Another way to handle big and small quantities

is with SI prefixes• SI prefixes modify units by powers of ten• For example kilo- (k) can be added to a unit to

make the unit larger by a factor of 1000One kilometer (km) equals a thousand meters

• In other words, “k” has a value of 1000 or 103 1 km = 1000 m = 103 m

• To convert km to m just substitute 103 for kExample: 5.2 km = 5.2(103)m = 5.2 103 m

SI Prefixes (cont.)• We can use kilo- with any unit to create units

a thousand times bigger:– second (s) kilosecond (ks)– gram (g) kilogram (kg)– newton (N) kilonewton (kN)

• Other prefixes like centi- (c) and milli- (m) make units smaller:

1 cm = (1/100) m = 10-2 m1 mm = (1/1000) m = 10-3 m

The Full Set of Prefixes

• SI Prefixes and scientific notation work well together to offer us more choices for clarity– Examples:

5.1 × 103 m = 5.1 mm

9.38 × 105 m = 9.38 × 102 km = 938 km

13700 g = 1.37 × 104 g = 13.7 kg

mill- meter

kilo- meter

kilo- gram

SI Prefixes and Sci. Not.

Common Prefixes• Of the 20 prefixes, only about half of them are

commonly used in science and industry• Here are the prefixes you should memorize:

Power Prefix Abbreviation109 nano- n106 micro- 103 milli- m102 centi- c103 kilo- k106 mega- M109 giga- G

Summary• Scientific notation uses powers of ten to express

large and small numbers more succinctly• Calculators help us use scientific notation• SI Prefixes allow us to create new units that are

powers of ten bigger or smaller• Scientific notation and unit prefixes together

give us a lot of choices and flexibility• We should memorize and use the most common

prefixes because they are part of the scientific language