Scientific Measurement Chapter 3 Scientific Measurement

Using and Expressing Measurements 3.1 A measurement a qty that has both a number and a unit. e.g. 10 kg fundamental to the experimental sciences. important to be able to make measurements and to decide whether a measurement is correct.

SI Units Need std units of measurement for scientists to report data in different parts of the world. SI units (revised metric system).

Base Units 7 base units in SI. base unit defined unit in a system of measurement that is based on an object or event in the physical world. independent of other units.

6 Base Units Quantity Base Unit Time Second (s) Length Meter (m) Mass Kilogram (kg) Temperature Kelvin (K) Amt of Substance Mole (mol) Energy Joule (J)

Time The SI base unit for time is the second (s). The frequency of microwave radiation given off by a cesium-133 atom is the physical standard used to establish the length of a second.

Prefixes To better describe the range of possible measurements, scientists add prefixes to the base units. metric system is a decimal system (multiples of 10).

Prefixes in SI Units Prefix Symbol Factor Scientific notation Example mega M 1,000,000 106 Mg; Mm kilo k 1,000 103 kg; km; kL deci d 1/10 10-1 dg; dm; dL centi c 1/100 10-2 cm milli m 1/1000 10-3 mm; mg

Length The SI base unit for length is the meter (m).

Mass Mass is a measure of the amt of matter. SI base unit of mass: kilogram (kg). A kg is about 2.2 lb.

Derived Units (1) e.g. the SI unit for speed is meters per second (m/s).

Derived Units (2) derived unit: A unit that is defined by a combination of base units e.g. m/s includes 2 SI base units—the m and s. Volume is in ‘m3’ and density is in ‘kg/m3’

Volume Volume the space occupied by an object. derived unit for volume: cubic meter (m3); cm3

Volume The cm3 works well for solid objects with regular dimensions but not for liquids or for solids with irregular shapes. 1 cubic decimeter (dm3) = 1 liter (L) 1 cm3 = 1 mL

Some common conversions 0°C = (0 + 273) K = 273 K 100°C = (100 + 273) K = 373 K 25°C = (25 + 273) K = 298 K

Volume  Liters (L) are used to measure the amt of liquid 1 L ≈ 1 quart.

Density Density a ratio that compares the mass of an object to its volume. units: g/cm3

Density If a sample of Al has a mass of 13.5 g and a volume of 5.0 cm3, what is its density? an intensive property can be used to identify an unknown sample of matter. Every sample of a pure sub has the same density.

Accuracy, Precision, and Error (1) 3.1 Accuracy and Precision Accuracy: a measure of how close a measurement comes to the actual value Precision: a measure of how close a series of measurements are to one another.

Accuracy and Precision

Accuracy and Precision

Using and Expressing Measurements 3.1 In scientific notation, a given # is written as the product of 2 # : a coefficient and 10 raised to a power e.g. estimate the # of stars in a galaxy

Accuracy, Precision, and Error (2) 3.1 To evaluate the accuracy (of a measurement), compared to the correct value. To evaluate precision, compare the values of 2 or more repeated measurements.

Accuracy, Precision, and Error (3) 3.1

Significant Figures in Measurements Measurements must always be reported to the correct # of significant figures because calculated answers often depend on the # of sig. fig. in the values used in the calculation.

Units and Quantities of temperature(1) 3.2 On Celsius scale the f.p. of H2O is 0°C and the b.p. is 100°C. On Kelvin scale the f.p. of H2O is 273 K (Kelvins), and the b.p. is 373 K. The zero point on the Kelvin scale, 0 K, or absolute zero, 0 K = 273°C

Units and Quantities of temperature (2) 3.2 1 degree on the Celsius scale ≡ 1 K on the Kelvin scale. to convert to K from °C, add 273 to convert to °C from K, minus 273

Units and Quantities of temperature (3) 3.2 Conversions Between the Celsius and Kelvin Scales These thermometers show a comparison of the Celsius and Kelvin temperature scales. Note that a 1°C change on the Celsius scale = 1 K change on the Kelvin scale.

Celsius and Kelvin Scales

Units and Quantities of Energy 3.2 The joule (J) is the SI unit of energy. One calorie (cal) is the qty of heat that raises the temperature of 1 g of pure water by 1°C.

Accuracy, Precision, and Error (7) 3.1 Just because a measuring device works, you cannot assume it is accurate. The scale below has not been properly zeroed, so the reading obtained for the person’s weight is inaccurate. The scale below has not been properly zeroed, so the reading obtained for the person’s weight is inaccurate. There is a difference between the person’s correct weight and the measured value. Calculating What is the percent error of a measured value of 114 lb if the person’s actual weight is 107 lb?

Conversion factor A ratio of equivalent measurements.

X by Conversion factor When a measurement is multiplied by a conversion factor, the numerical value is generally changed, but the actual size of the qty measured remain the same.

Dimensional Analysis A way to analyze and solve problems using the units, or dimensions, of the measurements. e.g. How many seconds are in one working day that lasts exactly eight hours? # of s = 8 hr x x = 28,800 s = 2.8800 x 104 s 60 s 60 min 1 min 1 hr

Addition (4.3 x 104) + (2.3 x 104) =

Addition (4.3 x 104) + (2.3 x 105) =

Answer: 2.73 x 10 5

Subtraction (4.3 x 104) – (2.3 x 104) =

Answer: ̶ 1.87 x 10 5

Subtraction (4.3 x 104) – (2.3 x 105) =

Multiplication (8.4 x 104) x (4.5 x 109) =

Answer: 3.78 x 10 14

Multiplication (8.4 x 104) x (4.5 x 10-9)

Answer: ≈ 3.78 x 10 -5

Division (8.2 x 104) ÷ (2.8 x 103) =

Answer: 2.9 x 10

Division (8.2 x 10-4) ÷ (2.8 x 10-3) =

Answer: ≈ 2.9 x 10 -1

The End