### THE SI system and units of measurement

```
SCIENTIFIC NOTATION
 Uses
exponential notation & places a decimal after
the 1st sig fig.
10n means “move decimal n places to right”
 10-n means “move decimal n places to left”
PRACTICE: (A) 5640
(B) 0.000150
5.64 X 10? = 5.64 X 103
1.50 X 10? = 1.50 X 10-4

COUNTING SIGFIGS IN SCIENTIFIC NOTATION
EXPONENTIAL TERM – NO SIG FIGS
 (IT ONLY MOVES THE DECIMAL PLACE)
 NUMBER-CONTAINS ONLY SIF FIGS
 EX.
7.809 X 104
4 SIG FIGS

3.40 X 10-6
3 SIG FIGS

What is the correct mass to report?
Measured Mass is _______________
SIGNIFICANT FIGURES
 Rules
for recognizing SigFigs:
When a number has a decimal:
Read Left to Right until you
Reach the first nonzero number
Then you begin counting SigFigs
Until you run out of digits (including any
zeros along the way)

Example: 0.003210 g
= _______ SigFigs?
SIGNIFICANT FIGURES
Practice:
 82.700 K
 0.000365 J
 3.034 g
 3.220 x 105 m
____sig figs
____sig figs
____sig figs
____sig figs
SIGNIFICANT FIGURES
 Rules for recognizing SigFigs:
When a number has no decimal:
Read Right to Left until you
Reach the first nonzero number
Then you begin counting SigFigs
Until you run out of digits (including any
zeros along the way)
 Example: 450300 m = _______ SigFigs?
SIGNIFICANT FIGURES
Practice:
 421 m
 800,890 J
 39,059,000 g
 523,000 L
____ sig figs
____sig figs
____sig figs
____sig figs
SIGNIFICANT FIGURES

Counted Quantites and Constants have absolute
values & we don’t count SigFigs
 Either
you counted the number of items right, or you
didn’t!
Example:
14 bananas
SIGNIFICANT FIGURES

1.
2.
3.
4.
5.
How many significant figures are in each of the
following numbers?
5.40 ng
1.2 x 103 mt
210 N
0.00120 mL
801.5 K
____
____
____
____
____
6.
7.
8.
9.
10.
0.0102 Amp
1,000 BTU
9.010 x 10-6 dm
101.0100 D
2,370.0 Cal
____
____
____
____
____
SIGNIFICANT FIGURES
 Why
are significant figures important
when taking data in the laboratory?
When you measure something, you never
get 100% accuracy on its measurement, so
you need a way to show just how accurate it
is.
SIGNIFICANT FIGURES
 Why
are significant figures NOT important
when solving problems in your math class?
In math, we assume that all numbers are
either 100% accurate, or that they are
constants, and thus have no uncertainty or
error involved in their creation.
SIGNFICANT FIGURES AND MATH
 We
will be required to do math with our
SigFigs
 Two
rule sets cover this:
Addition/Subtraction
And
Multiplication/Division
ADDITION AND SUBTRACTION SIG FIG RULES
line up the decimals
2. draw a line to the right of the number with
the least precision (shortest column)
3. answer can’t go past the line
4. use the 1st digit past the line to determine
where to round off
Example:
32.00 m + 48.1 m + 182.213 m = ????
1.
ADDITION AND SUBTRACTION SIG FIG RULES
line up the decimals
2.
draw a line to the right of the number with the least precision
(shortest column)
3.
answer can’t go past the line
4.
use the 1st digit past the line to determine where to round off
Example:
32.00 m + 48.1 m + 182.213 m = ????
1.
32.00 m
48.1 m
+____________
182.213 m
262.313 m
Must round to:
262.3 m
ADDITION AND SUBTRACTION SIG FIG RULES
1.
210.6 mm + 14.57 mm = ____________
2.
74.000 cm + 8.6 cm =____________
3.
0.0787 m + 0.85 m =____________
4.
84000 cm + 1110 cm =____________
5.
92008 g + 32100 g =____________
6.
8.000 mm + 0.0304 m =____________
7.
84.34 g - 5.2 g =____________
8.
9.81 cm - 3.151 cm =____________
9.
0.0900 n - 0.0094 n =____________
MULTIPLYING AND DIVIDING SIG FIG RULES

Answer can have no more SigFigs than
the factor with the fewest number of
SigFigs.
 This means that constants and
quantities do not affect sigfigs in the
answer!

Example: 127.3 x 42 = ???
MULTIPLYING AND DIVIDING SIG FIG RULES
1.
500 kg X 32 kg =____________
2.
680.0 n X 100. n =____________
3.
8560.0 g X 1000 g =____________
4.
4560 m X 0.100 m =____________
5.
85 kg X 0.001 kg =____________
6.
9200 L ÷ 873 L =____________
7.
0.85 2 kg2 ÷ 62 kg =____________
8.
985 g2 ÷ 500. g =____________
9.
10000 n2 ÷ 0.10 n =____________
10.
0.0006 g2 ÷ 25 g=____________
```