Exponential Notation

1
Exponential Notation

• Awesome to the power of ten!

2
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

3
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
4
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
5
Square Arrays
7 7 49 This equation can be written using
exponential notation.

• 49

7 is the base number. The exponent will be the
number of times you multiply 7 by itself. (in
this case 2) 7 7 49 or 7
2
6
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!

7
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.

8
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

9
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

10
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

11
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

12
Exponential Notation

• Find the value of the following numbers.
• 74
• 55
• 108
• 8
• 9

2401
3125
100,000,000
4
4096
3
729
13
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.

14
Fibonacci Sequence
A tiling with squares whose sides are successive
Fibonacci numbers in length
15
Did I Say Extra Credit?

• If you are interested, complete Math Masters page
  91 using patterns in Fibonacci Numbers