1. Scientific Notation

1. Why is it important? 1. Scientific Notation It’s useful in writing very small or large numbers. Every positive number X can be written as: (1 < N < 10) x 10some positive or negative integer Where N represents the numerals of X with the decimal point after the first nonzero digit.

2. 2. Positive Exponents • 101 = 10 • 102 = 10X10= 100 • 103 = 10X10X10 = 1000 • 104 = 10X10X10X10 = 10,000

3. 3. Negative Exponents • 10-1 = 1/10 = 0.1 • 10-2 = 1/100 = 0.01 • 10-3 = 1/1000 = 0.001 • 10-4 = 1/10000 = 0.0001

4. 4. Scientific Notation with Positive Exponents • We use the idea of exponents to make it easier to work with largeand small numbers. • 10,000 = 1 X 104 • 250,000 = 2.5 X 105 • Count places to the left until there is one number to the left of the decimal point. • 230,000 = • 35,000 = 2.3 X 105 3.5 X 104

5. 5. Scientific Notation with Negative Exponents 6 X 10-5 • 0.00006 = • 0.00045 = • Count places to the right until there is one number to the left of the decimal point • 0.003 = • 0.0000025 = 4.5 X 10-4 3 X 10-3 2.5 X 10-6

6. Multiplying with Scientific Notation • Add the Exponents • 102 X 103 = 105 • 100 X 1000 = 100,000

7. Multiplying with Scientific Notation (2.3 X 102)(3.3 X 103) • 230 X 3300 • Multiply the Coefficients • 2.3 X 3.3 = 7.59 • Add the Exponents • 102 X 103 = 105 • 7.59 X 105 • 759,000

8. Multiplying with Scientific Notation • (4.6 X 104) X (5.5 X 103) = ? • (3.1 X 103) X (4.2 X 105) = ?

9. Dividing with Scientific Notation • Subtract the Exponents • 104/103 = 101 • 10000X 1000 = 10

10. Dividing with Scientific Notation • (3.3 X 104)/ (2.3 X 102) • 33000 / 230 = 143.4783 • Divide the Coefficients • 3.3/ 2.3 = 1.434783 • Subtract the Exponents • 104 / 102 = 102 • 1.4347823 X 102 • 143.4783

11. Dividing with Scientific Notation • (4.6 X 104) / (5.5 X 103) = ? • (3.1 X 103) / (4.2 X 105) = ?