Scientific Notation

1. 7.1b  Determine scientific notation for small and big numbers. Scientific Notation

2. What is Scientific notation? • Use to express very • large numbers • The distance from • the Earth to the Sun • 152,000,000 km

3. What is Scientific notation? • Use to express very Small numbers. • The size of a hemoglobin cell • 0.0000000065 m

4. How do you write a number in scientific notation? A number written in scientific notation has two parts: 1 10x10x10x10 1st part: a number between 1 and 10 1  n < 10 1, 2,3, 4, 5, 6, 7, 8, 9. 2nd part: a power of 10 10⁴ = 10x10x10x10= 10,000 10⁻⁵= = 0.0001

5. In Scientific Notation, there are two kinds of exponents: positive and negative A positive exponent tells you: The number is greater than one Positive Exponent: 2.35 x 104 Negative Exponent: 3.97 x 10 -3 A negative exponent tells you:The number is less than one

6. From scientific notation to standard form, the exponent tells you how you should move the decimal point: If you have a positive exponent, move the decimal point to the right: 4 10 Positive Exponent: 2.31 x 104 2.31 x10x10x10x10 23.1 x10x10x10 231.x10x10 2310.x 10 23100. 2.31 x 104 2 3 1 = 0 0

7. From scientific notation to standard form, the exponent tells you how you should move the decimal point: Negative Exponent: 3.97 x 10-3 = 3.97 10x10x10 0.397 10x10 If you have a Negative exponent, move the decimal point to the Left: 0.0397 10 0 0 0 3 9 7 3.97x 10-3 0.00397 =

8. An easy way to remember this is: • If an exponent is positive: The number gets larger, so move the decimal to the right. • If an exponent is negative: The number gets smaller, so move the decimal to the left.

9. The exponent also tells how many spaces to move the decimal: 5 3 5 0 0 In this problem, the exponent is +4, so the decimal moves 4 spaces to the right.

10. The exponent also tells how many spaces to move the decimal: 0 0 0 0 4 0 8 10x10x10x10 In this problem, the exponent is -4, so the decimal moves 4 spaces to the left.

11. Try changing these numbers from Scientific Notation to Standard Notation: • 9.678 x 104 • 7.4521 x 10⁻3 • 8.513904567 x 107 • 4.09748 x 10-5 96780 0.0074521 85139045.67 0.0000409748

12. How do you change from Standard Notation to Scientific Notation: 1) First, move the decimal after the first whole number: 3 2 5 8 2) Second, add your multiplication sign and your base (10). x 3.258 10 3) Third, Count how many spaces the decimal moved and this is the exponent. 3 . 2 5 8 x 10 3 3 2 1

13. How do you change from Standard Notation to Scientific Notation: 4) See if the original number is greater than or less than one. • If the number is greater than one, the exponent will bepositive. 348943 = 3.489 x 105 • If the number is less than one, the exponent will be negative. 0.0000000672 = 6.72 x 10-8

14. Try changing these numbers from Standard Notation to Scientific Notation: • 9872432 • 0.0000345 • 0.08376 • 5673 9.872432 x 106 3.45 x 10-5 8.376 x 102 5.673 x 103

15. Order the following number from least to greatest, use scientific notation form. a) 3.5x10⁴, 3.5x10⁵, 3.5x10⁻² 3.5x10⁻², 3.5x10⁴, 3.5x10⁵ b) 5.3x10⁴, 3.5x10⁴, 35.0x10⁴ 3.5x10⁴, 5.3x10⁴, 3.5x10⁵ c) 5300, 53000, 0.000053 5.3 x10⁻⁶, 5.3x10³, 5.3x10⁴,