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 10N, where 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.
(What about the number 0? Can it be defined by scientific notation? Answer: NO!)
(What about the number 0? Can it be defined by scientific notation? Answer: NO!)
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 103 metres (in standard form) can be
written as 2 kilometres (2 km) where the prefix kilo (k) acts as 1000 or 103
4.
Other prefixes, their symbols and the
multipliers they represent are as follows:
Prefix Symbol Multiplier Value
of Multiplier
tera- T 1012 1 000 000 000 000
giga- G 109 1 000 000 000
mega- M 106 1 000 000
kilo- k 103 1 000
hecto- h 102 100
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 cm3 in m3 ?
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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 103 km
B.
3.14 x 108 nm
C.
3.14 x 1010 µm
D.
3.14 x 10-2 cm
4.
Convert:
a.
Density of sea water from 1.05 x 103 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 108 ms-1 (3 sf)
Updated on 24/01/2013 by tutortan1@gmail.com
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