Scientific Notation The basics and some math.

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

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) 9.13x E 8 coefficient = 9.13 exponent = 8 What is it?

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

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

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?

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

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

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

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

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

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