Scientific Notation The basics and some math.

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.

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) What is it?

coefficient = 9.13

9.13x10

8

9.13E

8 exponent = 8

First, let’s review exponents

  10 = 10 (x 1) 100 = 10 x 10 = 10 1 = 10 2   1,000 = 10 x 10 x 10 = 10 3 10,000 = 10 x 10 x 10 x 10 = 10 4 Count the “0”s 1 2 3 4  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

What does this really mean?

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

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 / 0.011 435 7 =  1,130,000,000  1.13 x 10 9

What does this really mean?

Scientific Notation Base 10 – negative exponents  If the exponent is negative, think division.

    10 -1 = 1/(10) 10 -2 10 -3 = 1/(10 x 10) =1/(100) = 1/(10 x 10 x 10) = 1/(1,000) = 0.1

= 0.01 = 0.001

10 -4 = 1/(10 x 10 x 10 x 10)= 1/(10,000) = 0.0001

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 = 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

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