1 figure estimated. 3 figures very certain. Units of Measurement:. CHAPTER 1 Introduction. Quantity Units Abv. time seconds s or sec. length meters m. mass kilograms kg. Example: Desk W idth76.74 cm. Measurement & Uncertainty. Hundreds ?
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1 figure estimated
3 figures very certain
Units of Measurement:
time seconds s or sec
length meters m
mass kilograms kg
Desk Width76.74 cm
Measurement & Uncertainty
Measurement w/ 4 significant figure accuracy
Misc – Prefixes to Memorize
M = mega = 106 1000,000
k = kilo = 103 1000
c = centi = 10-2 .01
m = milli = 10-3 .001
= micro = 10-6 .000 001
n = nano = 10-9 .000 000 001
NOTE: The prefix usually indicates a smaller value than the basic unit.
1 cm is smaller than 1 m
Misc – Prefixes to Use
1000,000m = 1 megameter = 1 Mm
1000m = 1 kilometers =1 km
1m = 100 centimeters = 1 x 102 cm
1m = 1000 millimeters = 1 x 103 mm
1m = 1,000,000 micrometers = 1 x 106m
1m = 1,000,000,000 nanometers = 1 x 109nm
W = 76.74 cm 1 m
W = .7674 m
W = .7674 m 1 km
W = .0007674 km
Still only 4 S/F
Leading zeros are not “significant”
Record zeros that were measured just like any other measured number
.4350 s 4 S/F
Waste of ink. Not measured, not significant
Conversion To Proper Units
NOTE: Still 4 S/F
Conversion To Other Units (to kilometers)
Significant Figures are figures that were measured.
.435 s 3 S/F
W = 76.74 cm 1 m 1 x 106 m
100 cm 1 m
W = 767400 m
Place holders are not measured and not significant
Still 4 significant figures
7 6 7 4 0 0 .m
Decimal point indicates the “trailing zeros” were measured.
Conversion To Other Units (to micrometers m)
What if you owned a very expensive and very precise measuring device and there really were zero tens and zero ones. How would you convey the information?
What if the tens are measured and equal zero, but the ones cannot be measured?
7.6740 x 105m
Through the use of scientific notation we can always convey the proper amount of significant figures.
SUMMARY – Test Yourself
Example 2: (34.3m/s) (21s)
× ÷ Least precise number determines the amount of significant figures in the answer.
Example 1: (4.3m/s) (49.317s)
= 212. 0631 m per your stupid calculator
= 210 m per our S/F rules
Reason: We can’t indicate a precision to our measurements that is misleading.
= 1.513235294 m/kg (stupid calculator)
= 1.5 m/kg (smart physics student)
Math Teacher Answer
Physics Teacher Answer
l1= 34.31 cm
l2 = 36.9? cm
NOTE: always means 2nd condition minus 1st condition
l = 36.9 cm
- 34.31 cm
The math teacher and your calculator assume zeros where none are shown.