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### CHAPTER 1Introduction

3 figures very certain

Units of Measurement:

QuantityUnitsAbv

time seconds s or sec

length meters m

mass kilograms kg

Example:

Desk Width 76.74 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

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

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?

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)

Math Operations w/ Sig. Figs.× ÷ 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

Math Operations w/ Sig. Figs.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.

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