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Note Pack #2 September 11, 2015 Aim: How to write very large or very small numbers? (Scientific Notation) Do now: How many stars do you think are in the universe? About – 912,493,737,239,013,813 What is Scientific Notation? 1) Scientific notation is a simple way of writing very large or very small numbers. Example 1: There are 912493737239013813 stars in the Universe or there are about 9.1 x 1017 stars Example 2: There are about 7,000,000,000,000,000,000,000,000,000 atoms in the human body or 7.0 x 1027 atoms in the human body Why do we use scientific notation? 1. Earth Science deals with a lot of large numbers. • It takes too long to write these numbers down and too much space on paper to write. • Doing math problems with these numbers can be very hard to do. How do we convert large numbers into scientific notation? • Let’s use this number 93,000,000. The average distance (in Miles) from the Earth to the Sun. Step 1. – Move the decimal between the first and second number. (count how many space you move it) 93000000 4 2 1 367 5 How do we convert numbers into scientific notation? (cont) Step 2. – drop all the number after the second number. If there is a non zero number after the second number then you must round up if the number is 5 or higher. 93000000 4 2 1 367 5 How do we convert numbers into scientific notation? (cont) Step 3. – add “x 10” to the number 93 x 10 Step 4 – place the number of times you moved the decimal to the power place next to the “10” 7 How do we convert small numbers into scientific notation? • When using very small numbers, the same steps apply except, instead of a positive exponent we use a negative exponent. Example 1 – A grain of sand weighs 0.0000265 grams or 2.65 x 10-5 grams Example 2 – A flea weighs .028 ounce or 2.8 x 10-2 ounce. How do we convert small numbers into scientific notation? • Let’s use 0.000078125 ounce. – the weight of a feather Step 1 – move the decimal to the right until you pass the first non zero number. (remember to count the spaces) 0 000078125 4 2 1 5 3 How do we convert small numbers into scientific notation? Step 2 – Drop all the numbers before the first whole number 0 000078125 4 2 1 5 3 How do we convert small numbers into scientific notation? Step 3 – add “x10” next to the number 78125 x 10 • Step 4 - place the number of times you moved the decimal to the power place next to the “10” • Step 5 – put a negative sign “-” in front of the exponent 5 How do we convert scientific notation into large numbers? • Let’s use this number 2.4 x 105 miles. The average distance (in miles) from the Earth to the Moon. Step 1 – Drop the x10. Step 2 – Move the decimal to the right the number of time the exponent is. Step 3 – Add the zero for each empty spot 5 24 0000 x 10 4 2 1 3 5 How do we convert scientific notation into small numbers? • Let’s use this number 3.1 x 10-4 grams. The average weight (in grams) of an ant. Step 1 – Drop the x10. Step 2 – Move the decimal to the left the number of time the exponent is. Step 3 – Add the zero for each empty spot 00031 x -4 10 4 2 1 3