__Standard Form / Scientific Notation / Prefixes__
1.
Scientists have developed a shorter method of
expressing very large or very small numbers known as the

**standard form**or**scientific notation**.
2.
By this method, all numbers are expressed in the
form of:

**A x 10**, where^{N}**A is an integer or decimal number**such that 1 ≤ A < 10 (A is equal to or greater than 1 but less than 10) and**N is an integer**(i.e. positive and negative whole numbers including zero). Hence,
o for
a number equals to A (where 1 ≤ A < 10),

**N equals to zero**;
o for
a number ≥ 10 (equals to or greater than 10),

**N is a positive integer**; and
o for
a number < 1 (less than 1),

**N is a negative integer**.
o for
a number which is negative, just insert a negative sign in front of the
notation.

3.
A

**prefix**is a letter placed before a unit of measurement to act as the multiplier of the unit – for example, 2000 metres or 2 x 10^{3}metres (in standard form) can be written as 2**kilo**metres (2**k**m) where the prefix**kilo**(**k**) acts as 1000 or 10^{3}
4.
Other prefixes, their symbols and the
multipliers they represent are as follows:

__Prefix__

__Symbol__

__Multiplier__

__Value of Multiplier__

tera- T 10

^{12}1 000 000 000 000
giga- G 10

^{9}1 000 000 000
mega- M 10

^{6}1 000 000
kilo- k 10

^{3}1 000
hecto- h 10

^{2}100
deca- da 10 10

deci- d 10

^{-1}0.1
centi- c 10

^{-2}0.01
milli- m 10

^{-3}0.001
micro- µ 10

^{-6}0.000001
nano- n 10

^{-9}0.000000001
pico- p 10

^{-12}0.000000000001

**(2006 P1 Q3 pg. 48 - convert 102.3 Mhz to Hz in standard form)**

**(2007 P1 Q1 pg. 92 - convert 470 pF to F in standard form)**

**(2008 P1 Q1 pg. 140 - convert 3.1 km/h to m/s)**

**(2009 P1 Q1 pg. 186 - given lengths in different prefixes - choose the longest)**

**(2010 P1 Q1 pg. 230 - pick prefixes in ascending order)****(2012 P1 Q2 pg. 332 - Which value is equal to 3 500 000 W?**Answer:

**B**

**3.5 MW)**

**(2013 P1 Q4 - What is the volume of 2.5**

**cm**

^{3}**in**

**m**

^{3}**?**

__-----------------------------------------------------------------------------__

__Segment Review Questions:__
A)

__Standard Form / Scientific Notation / Prefixes:__
1.
Express each the following physical quantities in its
SI unit and in scientific notation to 3 significant figures:

a.
Acceleration due to gravity, g = 9.783 ms

^{-2}
b.
Speed of light in vacuum, c = 298,000 kms

^{-1}
c.
Length of an onion cell, L = 0.000 028 m

d.
Charge of an electron = -1.6 x 10

^{-7}pC (pico coulombs)
2.
For each of the following symbol of prefixes, state its
name and its numerical value in index form (i.e. in power or exponential form):

a.
da

b.
h

c.
k

d.
M

e.
G

f.
T

g.
d

h.
c

i.
m

j.
µ

k.
n

l.
p

3.
Identify the largest and the smallest measurements from
the following values:

A.
3.14 x 10

^{3}km
B.
3.14 x 10

^{8}nm
C.
3.14 x 10

^{10}µm
D.
3.14 x 10

^{-2}cm
4.
Convert:

a.
Density of sea water from 1.05 x 10

^{3}kg m^{-3}to g cm^{-3}
b.
Velocity of cyclist from 5.6 m s

^{-1}to km h^{-1}
c.
Radio frequency from 102.3 MHz to Hz

d.
470 pF to F in standard form to 3 significant figures

e.
0.0006 Gm to Mm

f.
26 µm to mm

__Answers:__**1a)**g = 9.78 ms

^{-2}(3 sf)

**b)**c = 2.98 x 10

^{8 }ms

^{-1}(3 sf)

**c)**L = 2.8 x 10

^{-5 }m (3 sf)

**d)**e = -1.6 x 10

^{-19}(3 sf)

^{}

Updated on 24/01/2013 by tutortan1@gmail.com

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