1. Significant Figures, Measurements and Scientific Notation

2. Scientific Notation
-- used to express very large or very small numbers, and/or to indicate precision
(i.e., to maintain the correct number of significant figures)
Form: (# from 1 to 9.999) x 10exponent
800 = 8 x 10 x 10
= 8 x 102
2531 = x 10 x 10 x 10
= x 103 =
= 1.4 x 10–3

3. Change to scientific notation. 12,340 = 1.234 x 104
Put in standard form.
1.87 x 10–5 =
3.7 x 108 = 370,000,000
7.88 x 101 = 78.8
2.164 x 10–2 =
Change to scientific notation.
12,340 = x 104
0.369 = 3.69 x 10–1
0.008 = 8 x 10–3
1,000,000,000 = 1 x 109
6.02 x 1023 =
602,000,000,000,000,000,000,000

4. The Atlantic - Pacific Rule for Significant Figures
When determining the number of significant figures ask the question:
“Does the number have a decimal point?” (YES or NO answer)
If YES, then think of “P” for Present and the Pacific ocean
If NO, then think of “A” for Absent and the Atlantic ocean

5. The Atlantic and Pacific Rule for Significant Figures
Decimal Absent. Count right to left starting at first non-zero.
578,920,000
Pacific
Atlantic
Decimal Present.
Count left to right starting at first non-zero.

6. The Atlantic and Pacific Rule for Significant Figures
"P" for "Present".  This means that we imagine an arrow coming in from the Pacific ocean, from the left side
"A" for "Absent".  This means that we imagine an arrow coming in from the Atlantic ocean, the right side.

7. The Atlantic and Pacific Rule for Significant Figures
Look for the first non zero number starting from that direction
That number, and all other numbers following it are considered to be significant
For “P” the numbers to the right of the first non zero number
For “A” the numbers to the left of the first non zero number

8. Sig. Figs. Practice Ex 1) 0.020110 Ex 2) 730800 1) 48001 2) 98070001) 2) 3) 4) 5) 6) 7) 8)

9. Sig. Figs. Practice Ex 1) 0.020110 Ex 2) 730800 1) 48001 2) 98070001) 2) 3) 4) 5) 6) 7) 8)
Ex 1) (5 sig. figs.)
Ex 2) (4 sig. figs)
1) (5 sig. figs.)
2) (4 sig. figs.)
3) (4 sig. figs.)
4) (5 sig. figs.)
5) (2 sig. figs.)
6) (5 sig. figs.)
7) (7 sig. figs.)
8) (6 sig. figs.)

10. ( ) ______ How many cm are in 1.32 meters? equality: 1 m = 100 cm
(or 0.01 m = 1 cm)
conversion factors:
______
1 m
100 cm
______
1 m
100 cm or ( )
______
1 m
100 cm
1.32 m
= cm
We use the idea of unit cancellation
to decide upon which one of the two
conversion factors we choose.

11. Again, the units must cancel.
How many m is 8.72 cm?
equality:
1 m = 100 cm _
______
1 m
100 cm
______
1 m
100 cm or ( )
______
1 m
100 cm
8.72 cm
= m
Again, the units must cancel.

12. ( ) ( ) ____ ______ How many kilometers is 15,000 decimeters? 10 dm
1 km
15,000 dm
= km

13. How many seconds is 4.38 days?
____ ( ) ( )
_____ ( )
____
24 h
1 d
1 h
60 min
1 min
60 s
4.38 d
= 378,432 s
If we are accounting for significant figures, we would change this to…
3.78 x 105 s

14. Practice On your own convert the following measurements:
How many inches are there in 45.6 cm? (There are 2.54 cm in 1 inch)
How many hours are there in 34.5 years?
How many feet are in 5.3 yards?

15. Practice On your own convert the following measurements:
How many inches are there in 45.6 cm? (There are 2.54 cm in 1 inch)
18.0 inches
2. How many hours are there in 34.5 years?
3.02 x 105 hours
How many feet are in 5.3 yards?
15.9 feet

16. Book Problems
Pg. 52 # 37 a-e. Write in scientific notation and count the number of sig figs. # 49 a-e