Exponential
Notation
Awesome to the power of ten!
Square Arrays
• A square array is an array that has the same
number of rows as columns.
• A number that produces a square array is a
square number.
• 36 is a square number because you can create
the array
Square Arrays
• Which of these numbers can be arranged in a
SQUARE array?
14, 25, 46, 64
25 =
16 =
5 * 5 = 25
8 * 8 = 64
Square Arrays
• Which of these numbers can be arranged in a
SQUARE array?
49, 96, 77, 4
49 =
4=
2*2=4
7 * 7 = 49
Square Arrays
49 =
7 * 7 = 49
This equation can
be written using
exponential
notation.
7 is the base number.
The exponent will be the number of times
you multiply 7 by itself. (in this case 2)
2
7 * 7 = 49 or 7
Square Arrays
• You and a partner will have 3 minutes
to list as many square numbers as you
can.
• Find your partner.
• Pencils ready?
•Go!
Exponential Notation
• When you are squaring a number, you are
multiplying it by itself.
• Mathematicians use exponential notation to
count how many times you will multiply that
number by itself.
• For squared numbers you always multiply your
base number by itself twice.
Exponential Notation
• Your base number is the number you are
multiplying
3 will be our base number
• The exponent is the number of times you
multiply the base number by itself
4 will be our exponent – this means we will
multiply 3 by itself 4 times or 3 * 3 * 3 * 3
• We will write our value with exponential
notation like this:
3⁴
Exponential Notation
3⁴ is not a squared number because the
base number is multiplied more than
twice.
Find the value of the following numbers:
7⁴
3⁵
2⁸
Exponential Notation
Find the value of the following numbers:
3⁵ = 3 * 3 * 3 * 3 * 3
3*3=9
9 * 3 = 27
27 * 3 = 81
81 * 3= 243
Exponential Notation
Find the value of the following numbers:
2⁸
2 * 2 * 2 * 2 * 2 * 2 * 2 * 2=
2 * 2= 4 * 2 = 8 * 2 = 16 * 2 = 32 * 2 = 64 * 2 = 128 * 2 = 256
Exponential Notation
Find the value of the following numbers.
7⁴ = 2401
5⁵ = 3125
10⁸ = 100,000,000
8 4 = 4096
3
9 = 729
Fibonacci Numbers
• Can you figure out the pattern of the
following series of numbers?
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…
• These are Fibonacci Numbers. Fibonacci was really named
Leonardo of Piza. He wrote a book in 1202 that introduced
the idea of sequence into mathematics.
• His theory was that you can find the next number in the
sequence by adding the previous two.
Fibonacci Sequence
A tiling with squares whose sides are
successive Fibonacci numbers in length
Did I Say Extra Credit?
•If you are interested,
complete Math Masters
page 91 using patterns in
Fibonacci Numbers