Kind: captions
Language: en
In science, we often need to deal with
some very large numbers. For example,
the mass of the sun.
That is the mass of the sun. A two
followed by 30 zeros in units of
kilogram.
That is 2,000
billion billion billion kilograms.
There has got to be a better way to
write that. Can you imagine if there
wasn't?
And so we find that the mass of the sun
is 2 0 0 0.
Yes. Sorry. Could you repeat that? I was
with you up to 2000 0
uh
it was uh
2 0 0. So to represent large numbers
easily we use something called
scientific notation.
Scientific notation takes advantage of
powers of 10.
For example, 10 the^ of two means
take two 10 and multiply them together
and you get 100.
10 ^ of 3 means multiply three 10
together and you get a,000. 10 ^ 4 10
the^ 4 means take four 10
multiply them together
and you get 10,000.
So you should notice a pattern
developing. When it's 10 the^ of two,
our final answer has a one followed by
two zeros. When it's 10 the^ of three,
our final answer has a one followed by
three zeros. 10 the^ of four again four
zeros. So if we wanted to represent the
mass of the sun in scientific notation,
we would need 30 zeros. So we represent
that using 10 ^ of 30. This means we're
multiplying 10 by itself 30 times which
gives us a 1 followed by 30 zeros. But
the mass of the sun is actually twice
that. It's 2 followed by 30 zeros. So we
can multiply 2 by 10 30 in units of
kilogram and [snorts] that is the mass
of the sun. it's a lot easier to write
and it takes up much less space on the
page.
The other problem is we have to deal
with some very tiny numbers. For
example, the mass of a proton is
that is the mass of a proton. 0 and then
there's 26 zeros and then 1673 kg a
truly tiny number. So how do we deal
with this? Well again it's using a
similar trick. If we raise 10 to the
power of minus1
it means divide by 10 not multiply by
10. So this means divide by 10 which
gives you 0.1
10 ^ of minus2 means divide by 10 twice
which gives us 0.01
100th 10 ^ of minus 3 means divide by 10
three times
or 0.001.
So again you see a pattern developing.
The exponent here tells you the number
of places to the right of the decimal
that the one is. So in this case 10 the
minus2 the one is
two places to the right of the decimal.
Here 10us 3 the one is
three places to the right of the
decimal. So in this case I have a one
that is actually 27 places to the right
of the decimal. So I can write the mass
of a proton as
1.673
times 10us 27 kg.
And this 10us 27 has the function of
putting this number 1.673
uh 27 decimal places uh to the right of
the decimal point.
So as a challenge question to see if
you've understood it. If the sun were
made entirely of protons, how many
protons would there be in the sun?