Scientific NotationThe 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)

9.13x108

9.13E8

coefficient = 9.13

exponent = 8

What is it?

First, let’s review exponents

Count the “0”s

10 = 10 (x 1) = 101 1 100 = 10 x 10 = 102 2 1,000 = 10 x 10 x 10 = 103 3 10,000 = 10 x 10 x 10 x 10 = 104 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, 100 = 1

Scientific NotationBase 10 cont.

109 would equal a 1 followed by how many zeros?

9 1,000,000,000

What would 1.13 x 109 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 / 0.011 435 7 =

1,130,000,000

1.13 x 109

Scientific NotationBase 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?

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.