### Factor-Label Method

```Factor-Label Method
• Based on Conversion factors, which are
relationships between the units.
• A conversion factor is used to convert a unit
to any other related unit.
• The conversion factor is derived from the
equivalence statement of the two units.
 For example: 1 inch = 2.54 cm.
• It is a ratio equivalent
to 1
ALWAYS WORK THROUGH THE BASE UNITS!!!!!!!
• Example: 1 m = 100 cm
1m
100 cm
1m
100 cm
1m
100 cm
=
100 cm
1m
100 cm
1m
1
=
=
1
Conversion
factors
=
100 cm
=
1m
100 cm
=
1m
100 cm
• The correct choice is the one that allows the
cancellation of the unwanted units.
1m
Problem Solving Strategies:
•
•
•
•
1.
2.
3.
4.
Write the known value (given)
Draw the baseline (cross)
Write the wanted units (units of the answer)
Write the necessary conversion factors
•
If the unit to be eliminated is in the
numerator of the given information then that
unit should appear in the denominator of the
conversion factor, and vice versa.
Example:
•
•
•
•
How many milligrams are in 2 micrograms?
Step 1: Write the given.
Step 2: Draw the baseline
Step 3: Write the wanted units (units of the answer)
Step 4: Write the conversion factor(s).
 SINCE I DO NOT KNOW A DIRECT RELATIONSHIP,
I WORK THROUGH THE BASE UNIT
2 g
1g
1000 mg
1 000 000 g
1g
=
0.002 mg
Example: Given: 60 km/hr
Want: cm/s
60
60
60km
km
km
1000
1000
1000m
m
m
100
100 cm
cm
1 hr
11min
min
111hr
hr
hr
111km
km
km
11 m
m
60 min
60
60ss
=
== 1666.67 cm/s
cm/s
cm/s
Example: You are driving 65 mph
How many feet do you travel in this time?
1s
1 min
60 s
1 hour
65 miles
60 min
1 hour
65 miles
or
1 hour
5280 ft
1 hour =
1 mile
65 miles
95.333 feet
1 inch =
2.20 lb =
•
•
•
•
•
•
2.54 cm
1 kg
Convert the following quantities from one unit to another
30 m to mi
1500 yd to mi
206 mi to m
34 kg to lbs
34 lb to kg
20630
mim
5280
100
1500
feet
cmyd
34 kg
lb
12
1 inch
inch
3 feet2.2o
1 kg
2.54
1lbs
foot
1 cm
mile 1 mile
1m
=
= 15.4545
74.8
0.85227
= lbs
=0.018641
kg miles
331524.864
miles m
1mi
1m
2.54
1 foot
1cm
yd2.2o
1 kg
121lbs
5280
inch
inch feet5280
100feet
cm
In the lab we need to determine the
reliability of our measurements
2 ways
• Accuracy - how close is a measurement to the
true or correct value for the quantity.
▫ Percent error
• Precision - how close a set of measurements
for a quantity are to one another, regardless of
whether the measurements are correct.
▫ Significant digits
Accurate or Precise?!?!?
PRECISION
ACCURACY
 Reproducibility
 Correctness
 Check by repeating
measurements
 Check by using a different
method
 Poor accuracy results from
 Poor precision results from
procedural or equipment
poor technique
flaws
 Significant digits
 Percent Error
Consider the three sets of data below that have been
recorded after measuring a piece of wire that was
exactly 6.000 cm long.
SET X
5.864 cm
5.878 cm
SET Y
6.002 cm
6.004 cm
SET Z
5.872 cm
5.868 cm
•Which set of data is the most accurate?
•Which set of data is the most precise?
•Which set of data is more precise, set X or set Z?
Precise or Accurate?!?!?
• A nickel has a mass of 5.0 g.
• You measure it 4 times:
1. 1.05 g
2. 10.13 g
3. 6.28 g
4. 0.92 g
1.
2.
3.
4.
10.62 g
10.70 g
10.69 g
10.65 g
1.
2.
3.
4.
4.91 g
5.00 g
5.09 g
4.99 g
```