CHAPTER 1CHAPTER 1IntroductionIntroduction

Measurement & UncertaintyMeasurement & UncertaintyUnits of Measurement:Units of Measurement:

Quantity Units Abv time seconds s or sec

Example:Desk Width 76.74 cm

1 figure estimated3 figures very certain

Hundreds ?Tens 7Ones 6Tenths 7Hundredths 4Thousandths ?

Measurement w/ 4 significant figure accuracy

length meters m mass kilograms kg

MiscMisc – Prefixes to – Prefixes to MemorizeMemorize

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.

Example:Example:1 cm is smaller than 1 m

M = mega = 106 1000,000

MiscMisc – Prefixes to Use – Prefixes to Use

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 106 m

1m = 1,000,000,000 nanometers = 1 x 109 nm

1000,000m = 1 megameter = 1 Mm

Conversion To Proper UnitsConversion To Proper UnitsW = 76.74 cm 1 m

100 cm

W = .7674 m NOTE: Still 4 S/F

Conversion To Other UnitsConversion To Other Units (to kilometers)W = .7674 m 1 km

1000 mW = .0007674 km

Still only 4 S/F Leading zeros are not “significant”

Significant Figures are figures that were measured.

Other Examples:Other Examples:.435 s 3 S/F.4350 s 4 S/F

Record zeros that were measured just like any other

measured number0.4350 sWaste of ink. Not measured, not significant

Conversion To Other UnitsConversion To Other Units (to micrometers m)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

Question:Question: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?

Answer:Answer:7 6 7 4 0 0 . m Decimal point indicates

the “trailing zeros” were measured.

Question:Question:What if the tens are measured and equal zero, but

the ones cannot be measured?Answer:Answer:

7.6740 x 105 m

Through the use of scientific notation we can always convey the proper amount of significant figures.

SUMMARYSUMMARY – Test Yourself340 m340. m

34000 cm.340 km.34 km

.00034 Mm.000340 Mm

2 S/F3 S/F2 S/F3 S/F2 S/F2 S/F3 S/F

Math Operations w/ Sig. Figs.Math Operations w/ Sig. Figs.

× ÷ Least precise number determines the amount of significant figures in the answer.

Example 1: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.

Example 2:Example 2: (34.3m/s) (21s) (476kg)

= 1.513235294 m/kg (stupid calculator)

= 1.5 m/kg (smart physics student)

Math Operations w/ Sig. Figs.Math Operations w/ Sig. Figs.

+ - • Must round the more precise measurement to

the same precision as the least

• Units must be the sameExample:Example:

l1 = 34.31 cml2 = 36.9? cm

l = 36.9 cm - 34.31 cm

NOTE: always means 2nd condition minus 1st condition

Math Teacher Answer2.59 cm

Physics Teacher Answer2.6 cm

The math teacher and your calculator assume zeros where none are shown.