CHAPTER 1 Introduction

1. 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 Width 76.74 cm Measurement & Uncertainty Hundreds ? Tens 7 Ones 6 Tenths 7 Hundredths 4 Thousandths ? Measurement w/ 4 significant figure accuracy

2. 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

3. 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 106m 1m = 1,000,000,000 nanometers = 1 x 109nm

4. 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

5. 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?

6. Question: What if the tens are measured and equal zero, but the ones cannot be measured? Answer: 7.6740 x 105m 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

7. 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)

8. + - • 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.