Vastness of the Universe
Objects in the world we live in range in size
from the unimaginably large,
such as this
galaxy of stars,
which
measures
more than 1019
kilometers in
diameter.
Vastness of the Universe
to the incredibly small,
such as these
nickel atoms,
50 million of
which would
stretch across
the width of
your little
finger!
Managing Numbers
To help us keep track of such large and
small numbers, scientists make use of a set
of metric prefixes.
Here are a few examples:
kilo- means 1000 or 10 x 10 x 10 = 103
centi- means
1
1
−2
or
=10
100
10×10
Metric Prefixes
nano- means one-billionth or 10-9
milli- means one-thousandth or 10-3
centi- means one-hundredth or 10-2
kilo- means one thousand or 103
Mega- means one million or 106
Giga- means one billion or 109
Ratios
A ratio is a comparison of the numerical size
of two things.
The ratio of the length of the larger fish to the
smaller fish is 2:1
Ratios
Here's Mr. Dristle standing in front of his house,
holding a scaled model of his house.
The ratio of the model house to the real house
is 1:87
Ratios
Ratios also help us get a grasp on those
things that are very large or very small.
The ratio of the diameter of an atom to the diameter
of an apple is the same as the ratio of the diameter
of an apple to the diameter of the earth!
Ratios
There are as many
atoms in a normal
breath of air as
there are breathfuls
of air in the
atmosphere of the
Earth.
Ratios in Everyday Life
A recipe is more than a list of ingredients.
It's a list of ratios!
Foods are actually mixtures
of ingredients. Strictly
speaking, ratios don't have
to be held constant within
mixtures.
You can add salt or sugar to taste (within
reason) without totally ruining the product.
Ratios in Everyday Life
Suppose that a
pancake recipe
designed to feed three
people calls for 600 ml
of flour. How many
milliliters of flour would
you use if you wanted
to extend the recipe to
feed five people?
Ratios in Everyday Life
Solution: Set it up as a proportionality.
(A proportionality is just two ratios that are set
equal to each other.)
600 ml
x
=
3 people 5 people
x = 1000 ml of flour
Ratios in Nature
Chemical compounds are different from mixtures.
The atoms in chemical compounds are always
combined in never-changing ratios by nature.
The chemical formula tells us so, such as
H2O for water and CH4 for methane.
Ratios in Nature
When water is decomposed by electrolysis,
you will always get 2 liters of hydrogen for
every 1 liter of oxygen.
This is the ratio of
hydrogen to
oxygen by
volume.
The ratio by
weight is
different.
Ratios in Nature
According to the Periodic Table of the Elements, one
hydrogen atom weighs 1 atomic mass unit, while one
oxygen atom weighs 16 atomic mass units.
Since there are two hydrogen atoms in a water molecule,
the weight of the hydrogen is 2 x 1 or 2 a.m.u's.
There is only one oxygen atom, so the weight of the
oxygen in the water molecule is 16 a.m.u's.
Therefore, the ratio of hydrogen to oxygen in
any number of water molecules by weight is
2:16, which reduces down to 1:8.
Ratios in Nature
There are many hidden ratios in nature,
waiting to be discovered.
Ratios not only tell us much about the
underlying structure and orderliness of
our world, they also help us make
predictions for the future.