Measurement & Uncertainty

FUNDAMENTAL QUANTITYSI SYSTEM ENGLISH SYSTEM• Mass kilogram (kg) oz, lb, ton

• Distance meter (m) in, ft, yd, mi

• Temperature Kelvin (K) °F

• Time second (s or sec) sec, min, hr, day

• Amount mole (mol)

DERIVED QUANTITY (derived from the fundamental quantities above)• Area (distance)2 m2 in2, ft2

• Volume (distance)3 m3, L in3, yd3

• Velocity (distance/time) m/s mi/hr

• Density (mass/volume) g/L lb/in3

*See table 1.5 for metric prefixes! (Know Pico through Mega)

Temperature Scales

• Celsius to Kelvin conversion:TK = T°C + 273

• Kelvin to Celsius conversion:T°C = TK - 273

• Fahrenheit to Celsius conversion:T°C = (T°F - 32) ÷ 1.8

• Celsius to Fahrenheit conversion:T°F = (1.8 • T°C) + 32

Accuracy & Precision

Accuracy - how close the measurement is to the “true” value

Precision – how close individual measurements are to each other.

Accuracy

PERCENTAGE ERROR (PE)

observed value - accepted (true) value

= --------------------------------------- X 100%

accepted (true) value

How many significant digits are there?

1.4563 cm0.00123 m1.0058 sec1.54 x 1015m

8.500 mm5003 km100. L

5000 mL

Addition & Subtraction

cm 6.4

cm 012.0

cm 42.5

mL 6450

mL 85063

10.0 cm

78610 mL

Multiplying & Dividing

mm 00012.0 x 26400.5

sec125.2

2.4500 m

.00063 m2

2118 m/s

Dimensional AnalysisA problem solving method using a series of multiplications

and divisions

Multiply by fractions called “conversion factors”ALL conversion factors are equal to 1There is a table of conversion factors in the back cover of

your textbook

STEPS OF DIMENSIONAL ANALYSIS1) put the given AND the given unit on the left2) arrange conversion factors (fractions) to cancel ALL units

EXCEPT the required unit

For fractional units (m/sec)– work one unit at a time

For units to powers (m3) – take the ENTIRE conversion factor to that power