Measurements and Solving Problems
• 2.1 Units of Measurements The SI Measurement System 1. unit of measurement: physical quantity of
a defined size
2. standard of measurement: objects or natural phenomena of constant
value, easy to preserve and reproduce
Seven Fundamental SI Units 1. Length standard unit is the meter
meter: the distance light travels in a vacuum during a time
interval 2. Mass standard unit is the kilogram
3. Time standard unit for time is the second
4. Temperature based on Kelvin
5. Amount of substance : mole 6. Electric current: ampere 7. Luminous intensity: candela
Prefix Symbol Exponential factorGiga G 109
Mega M 106
Kilo k 103
Hecto h 102
Deca da 101
Deci d 10-1
Centi c 10-2
Milli m 10-3
Micro υ 10-6
Nano n 10-9
Units of measurement in calculations1. Factor-label method A problem solving method based on
using units as algebraic factors.
2. Unit conversion A ratio derived from the equality between
two different units and can be used to convert from one unit to the
other.
3. Examples: a. Convert 75 dollars to quarters 75 dollars x 4 quarters = 1 dollar
b. Convert 92 mg to g
92 mg x 1 g 1000 mg
=
c. Convert 25 cm to m.
d. Convert 72.0 g to micrograms
Derived SI Units1. A unit that can be obtained from combinations
of fundamental units.2. Volume The amount of space occupied by an
object
length x width x height cm x cm x cm = cm3
**** 1 L = 1000 mL = 1000 cm3
3. Density Relates the mass of substance to its
volume, or its mass per unit volume
density = mass volume
or d = m v
units for density: gases: kg m3
solid: g cm3
liquid: g mL
Example: 1. Find the density of a piece of aluminum
with a volume of 4.0 cm3 and a mass of 10.8 g. Is aluminum more dense or less dense than lead? (Dlead = 11.35 g/cm3)
2.2 Heat and Temperature 1. Temperature: is the measure of the
average kinetic energy of the particles in a sample of matter
2. Heat (heat energy): the sum total of the kinetic energies of
the particles in a sample of matter
3. Units of temperature degree Celsius water freezes at 0 °C water boils at 100 °C degree Fahrenheit water freezes at 32 °F water boils at 212 °F Kelvin K = 273 + °C
Temperature conversions: °C = 5/9 x ( °F -32)
°F = 9/5(°C) + 32
4. Units of heat a. joule (J): SI unit of heat
b. calorie: the quantity of heat required to raise the temperature of 1 g of
water 1 °C
**** 1 cal = 4.184 J
c. Ex. Convert 275 cal to joules and kilojoules. 1.
2.
5. Heat capacity and specific heat three things determine heat change 1. the nature of the matter changing
temperature
2. the mass
3. the size of the temperature change
heat capacity: amount of heat energy needed to raise the
temperature of a given sample of matter by one Celsius degree
specific heat: the amount of heat energy required to raise the temperature
of 1 g of a substance by one Celsius degree
• Common specific heats
equation: q = mCΔT
where q = heat (absorbed or released) m = mass C = specific heat ΔT = final temp – initial temp
Example: A 4.0 g sample of glass was heated
from 1 °C to 41 °C, and was found to have a specific heat of 0.20 J/g°C. How much heat was gained?
• 2.3 Using Scientific measurementsAccuracy and precisionAccuracy: refers to the closeness of a
measurement to the true or accepted value of the quantity measured
Precision: refers to the agreement among the numerical values of a set of measurements of the same quantity made in the same way
percent error: % error = accepted value – experimental value x 100 accepted value
Significant figures: See handout Reading scales:1. 2. 3.
• Quantitative Problems 1. How many cm are in 35 inches?
2. How many gallons are in 50 liters?
3. How many km/min is 32 mi/hr?