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# Chapter 2: Measurement

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1. Chapter 2: Measurement

2. 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)

3. 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

4. Prefixes (p. 26)

5. 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?

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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!

12. 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.

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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