Transcript 2 3 - Quia

1. How many four-cent postal cards 2. How far can you walk into a
are there in a dozen?
forest?
3. There was a blind beggar who
had a brother, but this brother
had no brothers. What was the
relationship between the two?
5. What mathematical symbol can
be placed between 2 and 3 so that
the resulting expression names a
number between 2 and 3?
4. If six glasses are arranged in a
straight line and the first three are
full of water and the last three are
empty, what is the fewest number
of glasses that can be moved so
that the glasses alternate:
empty, full, empty…?
6. A train that is one mile long
traveling at 60 mph enters a tunnel
that is one mile long. How long
until the train is out of the tunnel?
37 Mly away from Earth
That’s 37 Mega Light Years (ly)
1 ly is approximately 6,000,000,000,000 miles
or 6 trillion miles
1 Mly = 1,000,000 ly’s or 1 million light years
So this galaxy is
37 x 1, 000,000 x 6,000,000,000,000 miles away
If you’re curious that’s
222,000,000,000,000,000,000 miles or
222 quintillion miles
To give you some perspective that’s
39 sixtillion football fields
Chris Johnson ran for over
2,000 yards last year, the
most ever in a single season.
That’s 21 football fields. At that rate it would
take Mr. Johnson over…
1,000,000,000,000,000,000,000 record seasons
to run to the Sunflower Galaxy!
How can we rewrite extremely large
numbers in a way that makes mistakes less
likely?
base
n
a
5
2
exponent
(power)
72∙73
73∙74
82∙83
83∙84
52∙73
53∙64
x2∙x3
x3∙x4
a2∙a3
a3∙a4
x2∙y3
23∙y5
Law 1: When multiplying exponents with
like bases, we add the exponents.
Like bases
Unlike bases
22∙23 = 22+3 = 25
22∙33 = 2233
33∙34 = 33+4 = 37
33∙74 = 3374
x2∙x3 = x2+3 = x5
x2∙y3 = x2y3
22∙26
73∙77
236∙214
y3∙y3
a11∙a23
x43∙x16
7254∙7352
7452∙5473
72x4∙73x2
7x4∙73x7
x2y5∙xy3
a12b8∙a17b32
56
2
7,205,760,000,000,000
Law 2: A number or variable without an
exponent has an understood 1 as its
exponent.
2 = 21
x = x1
2∙23
3∙33
x∙x3
57
53
7493
7392
x8
x5
a27
a15
x5y4
x2y2
a7
b3
Law 3: When dividing exponents with like
bases, we subtract the exponents.
Like bases
Unlike bases
23
3-2 = 21 = 2
=
2
22
23
35
x7
7-3 = x4
=
x
x3
53
52
x3
x2
75y3
72y
x4y7
x2y4
22
73
23
35
57
57
73
73
a2
a2
x8
x8
x
x
Law 4: Any number or variable raised to
the zero power is 1.
20 = 1
x0 = 1