Download Conversions, Rounding, Sig Figs…Oh MY!!!

Conversions, Rounding,
Sig Figs…Oh MY!!!
Significant Figures
• The numbers we use in
science are measurements
• Significant figures result from
our inability to measure
precisely
Significant Figures
•All certain digits
•One final uncertain
digit (estimated)
16.
16. 7 mL
“Sig
*
Figs ”
Made
Easy
*Significant
Figures
Atlantic
Pacific
If a decimal point is present:
Pacific
Atlantic
If a decimal point is absent:
Pacific
Atlantic
Atlantic
Pacific
Decimal point is present:
4.3 2 SF
0.000520 3 SF
150.200 6 SF
Atlantic
Pacific
Decimal point is absent:
3 SF
153
4 SF
1 265 000
1 SF
1 000
Adding and Subtracting
30.254
+ 1.22
31.474
 31.47
30.254
– 0.0125
30.2415
 30.242
Multiplying and Dividing
• Sig figs limited by the least precise
measurement
– Exact conversion factors do not limit sig figs
30.45 m x 1.3 m =39.585 m2  40. m2
4 SF
2 SF
2 SF
PRACTICE
1.35 m x 2.467 m = 3.33 m2
55.46 g - 28.9 g = 26.6 g
1 035 m2  42 m = 25 m
Page 23
DIMENSIONAL
ANALYSIS
DIMENSIONAL ANALYSIS
• Treat units in
calculations as if they
were algebraic factors
DIMENSIONAL ANALYSIS
• Units must always be included in
the results of calculations
–Units also help you to check your
work as you go
36 weeks + 16 weeks
= 1 year
Conversion Factor
• A ratio equal to one
• Used to convert from one
dimensional unit to
another
Examples
• 1000m = 1 km
–1km/1000m or 1000m/1km
–Denisty = 2.5g/mL
• 2.5g/mL
1mL/2.5g
THE PROBLEM
“How many meters are
in 3.75 km?”
STEP #1: Restate the Problem
“How many meters are
in 3.75 km?”
? m = 3.75 km
STEP #2: Begin with the Known
Quantity
? m = 3.75 km
3.75 km
STEP #3: “ Make a Conversion
Grid”
? m = 3.75 km
3.75 km
1
STEP #4: Find the Correct
Units for the Conversion
Factor
? m = 3.75 km
Units to survive on top
3.75 km
1
* opposite
m
km
Units to cancel
on bottom*
STEP #5: Attach Numbers to
Units
? m = 3.75 km
1 km = 1 000 m
3.75 km
1
1 000
m
1
km
STEP #6: Do the Math!
? m = 3.75 km
3.75 km
1
1 000 m
km
1
=
Multiply 3.75 times (1 000  1)
Multiply (3.75 x 1 000) then  1
OR
STEP #7: Tah-Dah!
? m = 3.75 km
3.75 km
1
1 000 m
km
1
= 3 750 m
Don’t forget: Your answer must contain units!
How many . . .
• Millimeters in 1.574
meters
• Kilograms in 873
grams
• 1,125ft/min to mi/hr