1. Scientific Notation The basics and some math.

2. Take out your calculator.  Write these calculations and the answer in your notes:  12,922,341 / 0.011 435 7 =  1,130,000,000  0.05 / 20,111 =  0.000 002 486 Re-writing numbers in SCIENTIFIC NOTATION makes it so we don’t have to deal with all of these “extra” zeros.

3. Scientific Notation (Exponential Notation)  Scientific Notation is used to express any number as:  a number between 1 and 10  (called a coefficient)  multiplied by 10  (the “base” as in “base 10”)  raised to a power  (indicated by an exponent) 9.13x10 8 9.13E 8 coefficient = 9.13 exponent = 8 What is it?

4. First, let’s review exponents Count the “0”s  10 = 10 (x 1) = 10 1 1  100 = 10 x 10 = 10 2 2  1,000 = 10 x 10 x 10 = 10 3 3  10,000 = 10 x 10 x 10 x 10 = 10 4 4  The number in the exponent tells you how many times ten is multiplied by itself.

5. Reviewing Exponents  Any number raised to the 0 power – or has a 0 in the exponent = 1.  So, 10 0 = 1

6. Scientific Notation Base 10 cont.  10 9 would equal a 1 followed by how many zeros?  9  1,000,000,000  What would 1.13 x 10 9 be if written in “long form?”  Move the decimal place to the right 9 places.  1,130,000,000 What does this really mean?

7. When you have a positive exponent, move your decimal to the right the same number of places that are in the exponent.

8. Let’s rewrite the first number we calculated in scientific notation.  12,922,341 / 0.011 435 7 =  1,130,000,000  1.13 x 10 9

9. Scientific Notation Base 10 – negative exponents  If the exponent is negative, think division.  10 -1 = 1/(10) = 0.1  10 -2 = 1/(10 x 10)=1/(100) = 0.01  10 -3 = 1/(10 x 10 x 10)= 1/(1,000) = 0.001  10 -4 = 1/(10 x 10 x 10 x 10)= 1/(10,000) = 0.0001 What does this really mean?

10. Move the decimal point to the left if you have a negative exponent.

11. Let’s rewrite our second number in scientific notation.  0.05 / 20,111 = 0.000 002 486  Coefficient = 2.486  The decimal would have to be moved to the left 6 places, so our exponent will be - 6.  2.486 x 10 -6

12. Now give it a try with a partner. You have 5 minutes.