Measurements & Units
Significant Figures
• There is an uncertainty with every
measurement  reflect this in the number
of digits used in quoted results
• Do not count trailing or leading zeros
• Examples:
– 12.3 (3 sig figs)
– 1.23 (3), 0.45 (2), 0.00234 (3), 1200 (2)
– 4.56 •1015 (3)
Estimates
• Scientists often use a “back of the envelope”
calculation to get a sense for how big a
number should be
• Recipe: round every number involved up to
one sig fig and keep the exponent
Think inside the box!
• In essence, mathematics is a set of line by
line instructions
• Use them diligently, and a lot of problems
become mere exercises, i.e. tedious but
straightforward
Fermi Questions
• Attributed to Enrico Fermi
• Try to get the order of magnitude of a
quantity with very little data available
• Making a crude estimate is better than not
doing anything
Example: Parcel of the Earth
• The land area of the earth is divided up into
equal parcels for each person on earth. How
much would you get?
– Need area of earth
– Area of land
– # People on earth
Astronomical Measurements –
the Metric System
• Units of length:
– meter (m) 1 yd. 4 in.
– kilometer (km) = 1000 m or about 0.6 mi.
• Units of mass:
– kilogram (kg). 1 kg weighs about 2.2 lbs. (lb.=unit of
weight)
• Units of time:
– second, same as in the English system
Light Years and Parsecs
• A light year (ly) is the distance light travels in a year
– About 1016 m (~6 trillion miles)
• Speed of light is 3  108 m/sec or 186,000 mi/sec
– A unit of distance, not time!
– Observable universe is ~109 (10 billion) ly in diameter
• A parsec (pc) is a slightly larger unit of length
– 1 pc = 3.3 ly
The Universe is structured on
different length scales
Stars
nebulae
molecular clouds
star clusters
THE UNIVERSE
clusters
and
superclusters
galaxies
like the
Milky Way
quasars
Sun
planets
terrestrial
jovian
Solar System
black holes
pulsars
moons
comets
meteors
asteroids
dust
voids
Big  ----------------------------- small
Different lengths scales 
Different length units
• Human scale: meters (yards)
– Human height: 1.8 m
• Geographical scale: kilometers (miles)
– Distance to Cincinnati: 100 mi
• Solar system scale: Astronomical Unit
– Distance Earth-Sun: 1 A.U.
• Intragalactic scale: lightyears (parsecs)
– Next star: 4 lightyears
• Intergalactic scale: millions of lightyears (Megaparsecs)
– Andromeda galaxy: 2.2 million lightyears = 0.67 Mpc
• Cosmological Scale: billions of ly (Gigaparsecs)
– Edge of observable universe: about 15 billion ly
Different lengths scales 
Different length measurements
•
•
•
•
Human scale: yardstick
Geographical scale: triangulation
Solar system scale: Radar ranging
Intragalactic scale:
– Close stars: stellar parallax
– Far: spectroscopic parallax
• Intergalactic scale:
– Close: Variable stars
– Far: Tully-Fisher relation
• Cosmological Scale: Hubble’s Law
Units
• Dimensions and units are different!
• To convert from one unit to another use
conversion factors
– 2 miles = (2 mi)*(1)
= (2 mi)(1600 m/1 mi)
= 3200 m