Scientific Notation

Finish these equations 7000 = 7 x 10n 3 600,000 = 6 x 10n 5 30,000,000 = 3 x 10n 7 1.47 x 100 = 147 82 x 10,000 = 820,000 0.0629 x 1000 = 62.9

Scientific Notation Scientists use easy ways to write large numbers. This easy way is more compact & more useful. Scientific Notation This compact, useful method is called To write a number in Scientific Notation, express it as a product of two factors There are 2 criteria for writing a number in Scientific Notation:

Criteria: One factor is a number GREATER than or EQUAL to 1, but LESS than 10. (This will usually be a decimal) b. The other factor is a POSITIVE POWER of 10. Let’s look at an example: 93,000,000 Notice that the decimal point is moved until it reaches a number greater than 1, but less than 10.

93,000,000 in Scientific Notation is: 9.3 x 107 How many times was the decimal point moved to the left? That answer is your exponent. 93,000,000 in Scientific Notation is: 9.3 x 107 Steps: 1. Move the decimal point to the LEFT until you get to a number greater than or equal to 1, but less than 10. 2. Count the number of places moved- that is the power of 10.

185,000 1.85 x 105 Another example: Let’s try some: 120,000 1.2 x 105 4,064,000 4.064 x 106 25,000 2.5 x 104 714,500 7.145 x 105 1.56 x 108 156,000,000

How would you reverse Scientific Notation (write in standard form)? Do the OPPOSITE. Move the decimal point the number of places as the exponent in the Power of 10 to the RIGHT. 2. Add 0’s as place fillers. 3.6 x 103 3,600

Let’s try some 9.07 x 104 90,700 9 x 105 900,000 1.9 x 104 19,000 7.005 x 107 70,050,000 9.415 x 108 941,500,000

Scientific Notation can also be used to rename large decimals that are between 0 & 1 These numbers will use negative exponents for their powers of 10. Let’s look at an example: Follow these rules: First factor is greater than 1, but less than 10. 2. Second factor is a power of 10 with a negative exponent. The exponent depends on how many times you moved the decimal to the RIGHT. 0.00064= 6.4 x 10-4

1.24 x 10-4 6.9 x 10-3 Here’s another example: 0.0815 = 8.15 x 10-2 You try some: 0.015 = 0.0000086= 0.000124= 0.0069= 1.5 x 10-2 8.6 x 10-6 1.24 x 10-4 6.9 x 10-3

0.00000079 = 0.0000716 = 0.0045 = 7.9 x 10-7 7.16 x 10-5 4.5 x 10-3 It is now your turn to explain how to write numbers in scientific notation. Explain the process of scientific notation to the person next to you. Explain it using whole numbers & decimal between 0 & 1. Pretend that your partner does not understand this process, so explain it well & with examples!