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## Chapter 2: Measurement

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**Units of Measurement**• SI units • based on the International System of Units • Base unit • a defined unit based on an object or event in the physical world • Important Base Units to Know: • Time (second, s) Length (meter, m) • Mass (kilogram, kg) Volume (liter, L) • Temperature (Kelvin, K) • Density (grams/centimeter3, g/cm3)**Derived Units**Density and Volume are derived units meaning that they are combined units Ex. The volume of a block of wood can be determined by finding L x W x H therefore the units would be cm x cm x cm or cm3 Ex. Density is mass divided by volume or g/cm3**DENSITY**Density = mass volume Regular objects simply find the mass by using a balance and then find volume by measuring length, width, and height (plug and chug) What about irregularly shaped objects?**Density of Irregularly shaped objects**• Measure the mass by using a balance • How do you find volume? • WATER DISPLACEMENT METHOD • Fill a graduated cylinder with certain amount of water (30mL) • Slowly lower object into the graduated cylinder and measure the change in water level. • Ex. Suppose cylinder plus object has a volume of 32 mL • The change in volume is 2 mL therefore the volume of the object is 2 mL**Scientific Notation**• Expresses numbers as a multiple of two factors • A number between 1 and 10 • A ten raised to a power or exponent Ex. 5.0 x 103 5000**Calculations with Scientific Notation**• Addition and Subtraction-exponents must be the same so you will rewrite the number and then perform operation 4x102 + 5x103 = 4x102 + 50x102 = 54 x 102 or 5.4 x 103 • Multiplication- exponents do not have to equal instead perform operation on the factors and then add exponents (3 x 102) x (4 x 105) = 12 x 107 or 1.2 x 10 8 • Division- exponents do not have to be the same instead perform operation on the factors and then subtract exponents (1.5 x 105) / (3x103)= 0.5x102 or 5x101**Accuracy in Measurement**• You cannot be more accurate than the instrument in which you use to measure • Ex. A bathroom scale measures pounds to the 1/10. Will you ever be able to determine your weight to the 1/1000 with this particular scale? NO**Precision of Calculated Results**• calculated results are never more reliable than the measurements they are built from • Multi-step calculations: never round intermediate results! • General rules on rounding: • If it ends in 4 or below, round down to nearest whole number 52.63 52.6 • If it ends in 5 or up, round up to nearest whole number 52.67 52.7**Uncertainty in Measurements**• Making a measurement involves comparison with a unit or a scale of units • It is important to read between the lines • the digit read between the lines is always uncertain • convention: read to 1/10 of the distance between the smallest scale divisions • Significant Figures • definition: all digits up to and including the first uncertain digit • the more significant digits, the more reproducible the measurement is. • counts and defined numbers are exact- they have no uncertain digits!**Rules for Significant Figures**• 1. All digits are significant except for zeros at the beginning of the number and possibly terminal zeros. • 2. Terminal zeros to the right of the decimal point are significant • 3. Terminal zeros in a number without an explicit decimal point may or may not be significant. If doubt, write in scientific notation and then do significant figures. • 4. When multiplying or dividing, give as many significant figures in the answer as there are in the measurement with the least number of significant figures. • 5. When adding or subtracting measured quantities, give the same number of decimal places in the answer as there are in the measurement with the least number of decimal places.**Examples of the Rules**• Rule 1 example: 9.12 cm, 0.912 cm, and 0.00912 all have 3 sig fig • Rule 2 example: 9.000 cm, 9.100 cm, and 900.0 cm all have 4 sig fig • Rule 3 example: 900cm could have 1, 2, or 3 sig fig. If it was 900., then it would be 3. So, write it in sci. notation 9.00x102; therefore, 3 sig fig. • Rule 4 example: 4.1 x 5. =20.5=2. x101 • Rule 5 example: 184.2 +2.324 = 186.5**Conversions Between Units**• Use Factor Label Method aka Dimensional Analysis • Must know relationships among units • These relationships are called conversion factors Ex. 1000 mm = 1 m**Common Factors**1km=1000m kilometers to meters 1hm=100m hectometers to meters 1dam=10m decameters to meters 1m=1 m base 1m=10dm meter to decimeter 1m=100cm meter to centimeter 1m=1000mm meter to millimeter ** substitute any metric base in place such as liter**Common Factors**• Tera = 1012 Symbol: T • Giga = 109 Symbol: G • Mega = 106 Symbol: M • Kilo = 103 Symbol: k • Hecto = 102 Symbol: h • Deca = 101 Symbol: da • Deci = 10-1 Symbol: d • Centi = 10-2 Symbol: c • Milli = 10-3 Symbol: m • Micro = 10-6 Symbol: µ • Nano = 10-9 Symbol: n • Pico = 10-12 Symbol: p**How to Convert**EXAMPLE: 4.5 m = _________hm Xhm = 4.5 m x 1hm = 0.045 hm or 4.5x10-2 hm 100m 225 cm =________ mm Xmm = 225cmx10 mm= 2250 mm or 2.25 x 103 mm 1 cm Conversion factor is in red**Temperature Conversions**REMEMBER: Kelvin is SI base unit for temperature Celsius Kelvin K= oC+ 273.15 Fahrenheit Celsius oF=(1.8 x oC) +32 Fahrenheit Celsius Kelvin