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Scientificnotation

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Scientificnotation

1. 1. 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
2. 2. Scientists use easy ways to write large numbers. This easy way is more compact & more useful.This compact, useful method is calledTo write a number in Scientific Notation, express it as aproduct of two factorsThere are 2 criteria for writing a number in ScientificNotation:
3. 3. Criteria:•One factor is a number GREATER than or EQUAL to 1, butLESS 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.
4. 4. 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 107Steps:1. Move the decimal point to the LEFT until youget to a number greater than or equal to 1, but lessthan 10.2. Count the number of places moved- that is thepower of 10.
5. 5. Another example: 185,000 1.85 x 105 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 105 156,000,000 1.56 x 108
6. 6. How would you reverse Scientific Notation (write instandard form)? Do the OPPOSITE. 2.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
7. 7. Let’s try some9.07 x 104 90,7009 x 105 900,0001.9 x 104 19,0007.005 x 107 70,050,0009.415 x 108 941,500,000
8. 8. Scientific Notation can also be used to rename large decimals that are between 0 & 1These numbers will use negative exponents for theirpowers of 10. Follow these rules:Let’s look at an example: 3.First factor is greater than 1, but less than 10. 0.00064= 2. Second factor is a power 6.4 x 10-4 of 10 with a negative exponent. The exponent depends on how many times you moved the decimal to the RIGHT.
9. 9. Here’s another example:0.0815 = 8.15 x 10-2You try some:0.015 = 1.5 x 10-20.0000086= 8.6 x 10-60.000124= 1.24 x 10-40.0069= 6.9 x 10-3
10. 10. 0.00000079 = 7.9 x 10-7 0.0000716 = 7.16 x 10-5 0.0045 = 4.5 x 10-3It is now your turn to explain how to write numbers inscientific notation. Explain the process of scientificnotation to the person next to you. Explain it using wholenumbers & decimal between 0 & 1. Pretend that yourpartner does not understand this process, so explain itwell & with examples!