1. Scientific Notation

2. When scientists deal with very large numbers, it’s hard to keep track of place values!
How far?
miles

3. It is hard with very small numbers, too!
How wide is an atom?
meters wide!

4. Scientific notation consists of two parts:
A number between 1 and 10
A power of 10
N x 10x

5. We use Short hand ! one googol !!! 10 100 = 10 x 10
1,000 = 10 x 10 x 10
10,000 = 10 x 10 x 10 x 10
100,000 = 10 x 10 x 10 x 10 x 10
1,000,000 = 10 x 10 x 10 x 10 x 10 x 10
one googol !!!

6. Standard Form Scientific Notation
200 = 2 x 100
4,000 = 4 x 1000
70,000 = 7 x 10,000
500,000 = 5 x 100,000
3,000,000 = 3 x 1,000,000
Scientific
Notation

7. A short cut 8 000 000 . . Move the point to get a
number between 1 and 10
The point moved 6 places . .
Add the
decimal point
Between 1 and 10

8. A short cut 92 000 000 . . Move the point to get a
number between 1 and 10
The point moved 7 places . .
Add the
decimal point
Between 1 and 10

9. Try for yourself: Turn Standard Form into Scientific Notation
(1)
(2)
(3) 5 300
(4)
(5)

10. Add 5 zeros, although you probably won’t need them all.
Changing back
The point moves 5 places
3.46
00000 .
=346,000
Hint:
Add 5 zeros, although you probably won’t need them all.
Zeros after the point aren’t needed.

11. Add 7 zeros, although you probably won’t need them all.
Changing back
The point needs to move 7 places
8.6 .
=86,000,000
Zeros after the point aren’t needed.
Hint:
Add 7 zeros, although you probably won’t need them all.

12. Try for Yourself: Change Scientific Notation back to Standard form
(1)
(2)
(3)
(4)
(5) =
= 8 000 = = =

13. Standard Form to Scientific Form
for SMALL numbers
Move the point to get a
number between 1 and 10 .
The point moved 10 places. Negative sign for small numbers.

14. Standard Form to Scientific Notation
for small numbers
Move the point to get a
number between 1 and 10 .
The point moved 7 places. Negative sign for small numbers.

15. Standard Form to Scientific Notation
for small numbers
Move the point to get a
number between 1 and 10 .
The point moved 6 places. Negative sign for small numbers.

16. Change Standard Form to Scientific Notation
Try for Yourself:
Change Standard Form to Scientific Notation
(1)
(2)
(3)
(4)
(5)

17. Changing back small numbers Add 3 zeros to the left of the number.
Hint:
Add 3 zeros to the left of the number.
-3 so remember to move point left 3 spaces.
000 . 2
= 0.002 .

18. Changing back small numbers Add 5 zeros to the left of the number.
-5 so remember to move point left for small numbers.
Hint:
Add 5 zeros to the left of the number.
00000 .
8.6 =

19. Changing back small numbers Add 6 zeros to the left of the number.
-6 so remember to move point left for small numbers.
Hint:
Add 6 zeros to the left of the number.
000000 .
5.16 =

20. Change Scientific Notation to Standard form
Try for Yourself:
Change Scientific Notation to Standard form
(1)
(2)
(3)
(4)
(5) = = = = =