PhysicsLAB Resource Lesson
Metric Prefixes, Scientific Notation, and Conversions

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Common Metric Prefixes
Factor Name Symbol
109 giga G
106 mega M
103 kilo k
10-1 deci d
10-2 centi c
10-3 milli m
10-6 micro μ
10-9 nano n
10-12 pico p
 
Given below is an expanded diagram of a meter stick showing the relationships between meters, decimeters (10-1 m), centimeters (10-2 m), and millimeters (10 -3 m).
 
relationship between meters, dm, cm, and mm
 
 
Scientific Notation
 
The easiest way to convert one unit of measurement to another unit of measure is to initially convert its metric prefix to its associated power of ten while also rewriting the original numerical value in scientific notation. The final answer can then be simplified by just combining exponents.
 
A number is expressed in scientific notation when it is in the form
a × 10n where 1≤ a <10 and n ∈ { ... -3, -2, -1, 0, 1, 2, 3 ... )
Before continuing with the next section of lesson in which we convert measurements in one metric prefix to another, let's practice converting between decimal notation and scientific notation.

Refer to the following information for the next five questions.

Express the following numbers in scientific notation.
 362

 11.8

 0.00362

 0.118

 1986

Refer to the following information for the next four questions.

Convert these numbers in scientific notation to decimal form.
 8.71 x 10-3

 2.56 x 102

 1.28 x 106

 5.21 x 10-4

 
Basic Conversions
 
Before looking at some examples of converting measurements from one metric prefix to another we need to remember the following rules for working with exponents:
Rules of exponents:
  • 10x × 10y = 10(x + y)
  • 10x ÷ 10y = 10(x - y)
  • 10-n = 1 ÷ 10n
 
Example #1
628 nm = ? meters
628 nm = 628 × 10-9 meters [definition of the metrix prefix nano]
628 nm = 6.28 × 102 × 10-9 meters
628 nm = 6.28 × 102+(-9) meters
628 nm = 6.28 × 10-7 meters
Example #2
628 nm = ? μm
using the answer to Example #1 we can replace 628 nm with 6.28 × 10-7 meters
6.28 × 10-7 meters = ? μm
since 1 μm equals 10-6 meters, we rewrite -7 as -1+(-6)
6.28 × 10-1+(-6) meters = ? μm
remember that adding exponents means multiplying powers of 10
6.28 × (10-1 × 10-6 ) meters = ? μm
(6.28 × 10 -1) × (10-6 meters) = 6.28 × 10-1 μm = 0.628 μm
 
Now you practice two conversions problems.
 
 1. How many mm are in each of the following measurements: 500 μm, 50 cm, 5 m?

 2. Rank the following from smallest to largest:  500 µm, 50 cm, 50 dm, and 5 mm.

 
Some Advanced Conversions
 
Example #3
If a liter equals 1000 cm3, then a cube that is 100 cm on each edge would hold how many liters?
 
V = l w h = (100 cm)3 = (102 cm)3 = 106 cm3
our question has now become how many liters are in 106 cm3
106 cm3 = ? L
since 1 L = 103 cm3, we rewite 6 as 3+3
10(3+3) cm3 = ? L
remember that adding exponents means multiplying powers of 10
(103× 103) cm3 =  ? L
103× (103 cm3) = 103 L
Example #4
How many m3 does a cube 100 cm on an edge occupy?
 
V = l w h = (100 cm)3 = (102 cm)3 = 106 cm3
V = l w h = (100 cm)3 = (1 m)3 = 1 m3
 
Therefore, 106 cm3 = 1 m3
Example #5
How many m3 are present in a cube having a volume of 1000 cm3?
 
1000 cm3 = 103 cm3 = ? m3
using the answer to Example #4 we know that 106 m3 = 1 m3
103 cm3 = 10(-3+6) cm3 = ? m3
remember that adding exponents means multiplying powers of 10
(10-3 × 106) cm3 = ? m3
10-3 × (106 cm3 ) = 10-3 m3



 
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