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Exponential Notation

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.

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Exponential Notation

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  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

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