PHY101 CHAPTER 1 Measurement Unit Significant Figures Dimensional Analysis 1.1. Measurement Units • SI - International Metric System • US - Customary System • Basic Metric Units Quantity Length Mass Time El. Current Temperature Unit meter kilogram second Ampere Kelvin Symbol m kg s A K SI Prefixes Power Prefix Symbol 10-18 atto a 10-15 femto f 10-12 pico p 10-9 nano n 10-6 micro 10-3 milli m 103 kilo k 106 mega M 109 giga G 1012 tera T 1015 peta P 1018 exa E Metric Line METRIC LINE Tm Gm Mm km m mm um nm pm fm am Length Tg Gg Mg kg g mg ug ng pg fg ag Mass Tl Gl Ml kl l ml ul nl pl fl al Capacity T - tera G - giga M - mega k - kilo Center m - milli u - micro m - meter n - nano g - gram p - pico l - liter f - femto Conversion Table METRIC TO ENGLISH ENGLISH TO METRIC From Metric To English Multiply by From English To Metric Multiply by meters yards 1.09 yards meters 0.91 meters feet 3.28 feet meters 0.30 centimeters inches 0.39 inches centimeters 2.54 kilometers miles 0.62 miles kilometers 1.61 grams ounces 0.035 ounces grams 28.35 kilograms pounds 2.20 pounds kilograms 0.45 liters quarts 1.06 quarts liters 0.95 liters gallons 0.26 gallons liters 3.78 Temperature Conversion Converting Fahrenheit to Celsius 5( F 32) C 9 Converting Celsius to Fahrenheit 9C F 32 5 Conversion in Metric system • Example 1: Convert 50 • Example 2: A hall mph to m/s. bulletin board has an area of 2.5 m2. What is this From 1 mile = 1609 m: area in cm2? Because 1m=100cm it is 50m 1609m 1h 22m / s sometimes assumed that h m 3600 s 1 m2 = 100 cm2, which is WRONG. The correct conversion is: 2.5m2 2.5m m 2.5 100cm 100cm 25000cm2 2.5 104 1.2. Significant Figures The number of significant figures of a numerical quantity is the number of reliably known digits it contains. • Zeros at the beginning of a number are not significant. They merely locate the decimal point. – 0.254 m - three significant figures (2, 5, 4) • Zeros within a number are significant – 104.6 m - four significant figures (1, 0, 4, 6) • Zeros at the end of a number after the decimal point are significant: – 2705.0 m - five significant figures (2, 7, 0, 5, 0) Significant Figures - Conclusion • The FINAL result of a multiplication or division should have the same number of significant figures as the quantity with the least number of significant figures that was used in the calculation. • The FINAL result of the addition or subtraction of numbers should have the same number of decimal places as the quantity with the least number of decimal places that was used in the calculation. Significant Figures - Practice • Example 1: Find the area of a room 2.4 m by 3.65 m: 2.4m x 3.65m = 8.76m2=8.8m2 Rounded to 2 sf - because 2 is least # of sf • Example 2: Given the numbers 23.25, 0.546, and 1.058 – add the first two – subtract the least number from the first 1.3. Dimensional Analysis • The two sides of an equation must be equal not only in numerical value, but also in dimensions (BOTH SIDES OF THE EQUATION ARE NUMERICALLY AND DIMENSIONALLY EQUAL). And dimensions can be treated as algebraic quantities. • [L] - Length • [M] - Mass • [T] - Time Dimensional Analysis - Practice • Example 1: Is an equation • Example 1: Is an equation x = v t a correct equation? x = a t2 a correct equation? – x - is the distance in m – a is acceleration in m/s2 – v = is the velocity in m/s [ L] – t - is the time in s [ L] [T 2 ] [ L] [T 2 ] Dimensionally the equation is: [ L] [ L] [T ] [ L] [T ] Practice • Show that the equation x • Determine the number of = xo + vt, where v is significant figures: velocity, x and xo are – 1.007 m lengths, ant t is time, is – 8.03 m dimensionally correct – 16.272 kg • A Boeing 777 jet has a – 0.015 µs length of 209 ft. 1 inch, • The two sides of right and wingspan of 199 ft triangle are 8.7 cm (two and 11 inches. What are significant figures) and these dimensions in 10.5 cm (three significant meters? figures). What is the area of the triangle?
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