## Tuesday, 27 March 2012

### Standard Form / Scientific Notation / Prefixes

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!)

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

Solving Problems Involving Conversion of Units of Measurements – Sound Understanding of the Prefixes and Some Basic Mathematical Skills Are Needed.

(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