Topic 1.2 Units & Measurement
What are
some
examples?
Mile, furlong, fathom, yard, feet, inches,
Angstroms, nautical miles, cubits
There are seven fundamental base units
which are clearly defined and on which all
other derived units are based:
You need to know these

This is the unit of distance. It is the distance
traveled by light in a vacuum in a time of
1/299792458 seconds.

This is the unit of time. A second is the
duration of 9192631770 full oscillations of
the electromagnetic radiation emitted in a
transition between two hyperfine energy
levels in the ground state of a caesium-133
atom.

This is the unit of electrical current. It is
defined as that current which, when flowing
in two parallel conductors 1 m apart,
produces a force of 2 x 10-7 N on a length of
1 m of the conductors.

This is the unit of temperature. It is 1/273.16
of the thermodynamic temperature of the
triple point of water.

One mole of a substance contains as many
molecules as there are atoms in 12 g of
carbon-12. This special number of molecules
is called Avogadro’s number and equals 6.02
x 1023.

This is the unit of mass. It is the mass of a
certain quantity of a platinum-iridium alloy
kept at the Bureau International des Poids et
Mesures in France.
THE kilogram!


This is the unit of luminous intensity. It is the
intensity of a source of frequency
5.40 x 1014 Hz emitting 1/683 W per steradian.
The candela is not used in the IB Diploma
Program
Other physical quantities have units that are
combinations of the fundamental units.
Speed = distance/time = m.s-1
Acceleration = speed/time = m.s-2
Force = mass x acceleration = kg.m.s-2
(called a newton)
(note in IB we write m.s-1 rather than m/s)
1 N = kg.m.s-2
(F = ma)
1 J = kg.m2.s-2
(W = Force x distance)
1 W = kg.m2.s-3
(Power = energy/time)
It is sometimes useful to express units that are
related to the basic ones by powers of ten
See “Data
Booklet”
from
Myclass site
3.3 mA = 3.3 x 10-3 A
545 nm = 545 x 10-9 m = 5.45 x 10-7 m
2.34 MW = 2.34 x 106 W
If an equation is correct, the units on one side
should equal the units on another. We can
use base units to help us check.
For example, the period of a pendulum is
given by
T = 2π l where l is the length in metres
g and g is the acceleration due to gravity.
In units
m
=
m.s-2
s2
=
s

How many significant figures are in the
following measurements?
 425.5 m
 0.00043 s
 1500 kg
 0.006580 A
 273.00 K
 17.04 m.s-1

Calculate the following with the correct
number of sig figs in your answer

13cm + 8.20cm + 0.7051cm

1.500m x 2.01m x 0.5520m




Sig figs give an indication of the degree of
precision for a measurement and/or a
calculation
All digits in the measurement are certain,
plus the first estimated (uncertain) digit
ONLY used when a number is (or is assumed
to be) a measured quantity
EXACT quantities do not have sig figs
 i.e.; discrete data
 For
measurements smaller than 1:
◦ 0.004530
 For
measurements smaller than 1:
◦ 0.004530
Find the first zero on the left-most side
 For
measurements smaller than 1:
◦ 0.004530
From that place onwards, all numbers are
significant!
 For
measurements greater than 1:
◦ 45300
 For
measurements greater than 1:
◦ 45300
Start with the first digit
 For
measurements greater than 1:
◦ 45300
Go right to the last integer, all non zeros
are significant
 For
measurements greater than 1:
◦ 45300.
Or look for a decimal point, now all
numbers are significant
Note: we assume that all digits in the
textbook are significant
eg; 100 kg has 3 s.f.
 For
measurements greater than 1:
◦ 45300
You may see a line instead of a decimal
In this case, all numbers up to the line
are significant
**Remember, sig figs tell the reader the
precision in your measurements**

How many significant figures are in the
following measurements?
 425.5 m
 0.00043 s
 1500 kg
 0.006580 A
 273.00 K
 17.04 m.s-1
4
2
2 (1500.  4)
4
5
4

When adding or subtracting:
◦ Your answer must have the same degree of
precision as the least precise measurement
◦ That means your final answer needs to be
rounded to the fewest number of decimal places
from your measurement

When multiplying or dividing:
◦ The number of sig figs in the answer is equal to
the least number of sig figs in any of the
measurements used in the calculation
◦ NEVER round any numbers until your final
answer!



Calculate the following with the correct
number of sig figs in your answer
13.1cm + 8.202cm + 0.70512cm
22.0cm
1.500m x 2.01m x 0.5520m
1.66m3
Page 6
Questions 15, 16, 18, 19
Reading: Internal Assessment Guide, DCP Part 1