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CHAPTER 1 Introduction

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1 figure estimated

3 figures very certain

Units of Measurement:

CHAPTER 1Introduction

QuantityUnitsAbv

time seconds s or sec

length meters m

mass kilograms kg

Example:

Desk Width76.74 cm

Measurement & Uncertainty

Hundreds ?

Tens 7

Ones 6

Tenths 7

Hundredths 4

Thousandths ?

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.

Example:

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

100 cm

W = .7674 m

W = .7674 m 1 km

1000 m

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

0.4350 s

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.

Other Examples:

.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

Answer:

7 6 7 4 0 0 .m

Decimal point indicates the “trailing zeros” were measured.

Conversion To Other Units (to micrometers m)

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?

Question:

What if the tens are measured and equal zero, but the ones cannot be measured?

Answer:

7.6740 x 105m

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

SUMMARY – Test Yourself

340 m

340. m

34000 cm

.340 km

.34 km

.00034 Mm

.000340 Mm

2 S/F

3 S/F

2 S/F

3 S/F

2 S/F

2 S/F

3 S/F

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

(476kg)

× ÷ 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)

+ -

- Must round the more precise measurement to
- the same precision as the least
- Units must be the same

Math Teacher Answer

2.59 cm

Physics Teacher Answer

2.6 cm

Example:

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.