1. Simplify the following
Write all the answers using positive exponents. 1)
= 1
2) – 7w 0
= – 7 3) 4) 5)

2. Scientific Notation

3. Scientific Notation Form
Scientific Notation is used to write very large and very small numbers.
Numbers like:
93,000,000
Scientific Notation Form
where a > 1 and a < 10
and
n is an integer

4. a × 10 n Scientific Notation Form
To write an number in scientific notation form,
move the decimal point until a number between 1 and 10 is reach.
This is the “a” value.
To find the “n” value. Count the number of decimal places moved.
“n” is positive if the decimal was moved to the left. “n” is negative if the decimal was moved to the right.

5. a × 10 n Scientific Notation Form S.N. 9.3 × 10 7 2.5 × 10 – 5
Write the following numbers in S.N.
93,000,000
There’s no decimal point, place one at the end.
93,000,000.0
Move the decimal point between the 9 and 3 and count the number of decimal places moved.
9.3 × 10 7
Move the decimal point between the 2 and 5 and count the number of decimal places moved.
2.5 × 10 – 5

6. To write a S.N. number without the exponents, move the decimal point “n” places.
Move the decimal to the left if “n” is negative.
Move the decimal to the right if “n” is positive.
1.86 × 10 5
= 186,000
Move the decimal 5 places to the right.
8.2 × 10 – 7 =
Move the decimal 7 places to the left.
4 × 10 3
= 4,000
9 × 10 – 5 =

7. To find the product or quotient of numbers written
in S.N., find the product or quotient of the “ a ” terms and of the “ 10 n “ terms.
( 2 × 10 3 )( 3 × 10 5 )
= ( 2 · 3 ) × ( 10 3 · 10 5 )
= 6 × 10 8
( 8 × 10 – 2 )( 4 × 10 9 )
= ( 8 · 4 ) × ( 10 – 2 · 10 9 )
= 32 × 10 7
= × 10 8
6 × 10 8 6
10 8
_______
___
____ ×
= 3 × 10 5 =
2 × 10 3 2
10 3
10 2
2 × 10 2 2
________
___
____ = ×
= 0.4 × 10 9
= 4 × 10 8
5 × 10 – 7 5
10 – 7

8. Try This:
Write the following in Scientific Notation
25000
= × 10 4
Write the following without Scientific Notation
8 × 10 – 5 =
Simplify
( 3 × 10 2 )( 6 × 10 – 8 )
= 18 × 10 – 6
= 1.8 × 10 – 5
9 × 10 7
________
= × 10 1
2 × 10 6