Analytical skills Flashcards
Base units + measurements
- Magnitude?
- Orders of Magnitude?
- Unit?
- Standard form?
- A Magnitude – size of the number
- Orders of Magnitude - the approximate size of a quantity/measurement
- A Unit – based on a comparison with an agreed standard (convert to same unit)
-
Standard form as: A x 10^n
(A has to be a whole number between 1-10)
What are the 2 standards/ types of scientific measurements?
-
SI Base quantities
(international system of units - system of agreed units, recognised by everyone + used in science, industry + medicine) -
The Metric system
(Modern approach to units)
1.
The international system of units
SI
What are the 7 base units + their symbols?
THE SI BASE UNITS:
- Electric current: Ampere (A)
- Luminous intensity: Candela (cd)
- Thermodynamic temperature: Kelvin (K)
- mass: Kilogram (Kg)
- length: Metre (m)
- amount of substances: Mole (mol)
- time: Second (s)
Quantity: base unit (symbol)
- Derived SI based units?
- Base units for these?
Derived (SI) units
- units defined by a combination of base units
(eg metres pr second [m/s^-1], metres squared for area)
Base units r based on an absolute standard that’s easily reproducible
- All other units are derived from the base units = known as derived units
EG
- Speed (ms-1- metres pr second) is a derived unit
= it uses two base units: metre and second - Density = kgm-3
- Pressure = N/m2
2.
The metric system
- A Modern approach to weights + measures
- Uses units such as metres, litre, gram to measure length, liquid volume +mass
Property - Unit - Symbol
- Length - metres - m
- Mass - gram - g
- Volume - Litre - L
- Time - second - S
- Temperature - celsuius - °C
Metric system prefixes
- Based on the powers of 10 to express multiples /subdivisions of units
- SI base units can be converted into more appropriate units for the quantity being measured, by adding a prefix to the name of the base unit
2.56 cm
C – the prefix (centimetres)
m – the unit (metres)
1 cm3 = 1 mL = 0.001 L
Metric conversions
- cm –> dm [/10] –> m [/10]
- cm2 –> dm2 [/100] –> m2 [/100]
- cm3 –> dm3 [/1000] –> m3 [/1000]
LEARN CONVERSIONS BETWEEN UNITS
CHECK ‘REVISION’ PPT ON CANVAS FOR PRACTICE
Errors
Accuracy?
- Accuracy is a measure of how close values are to the accepted standard value for a quantity
- Is also know as trueness
Precision?
- Precision the closeness of two or more measurements to each other
- EG u weigh a substance 5 times + get 3.2 g each time
- Precision is independent of accuracy
List ways of improving the precision of
measurements
- Using instruments with finer scale divisions
- Repeat reading = 3 repeats + take average
- Record figures correctly
- Measuring/counting a group of >10 - Using large sample sizes
- Checking for zero errors
- Checking calibration of instruments
- Make sure equipment used is clean, no air bubbles etc
errors (±) can be expressed as ‘absolute’ errors or as a%
Absolute error?
- Absolute Error is the difference between the actual + measured value
- Absolute error = ½ x smallest division (of the measurement)
EG 8.3 ± 0.05cm [as it was going up by 0.1cm]
ALWAYS NEED TO ADD THE ± SIGN OR LOSE MARKS
Relative error?
- Relative Error is the Absolute Error divided by the actual measurement
- Relative error = Absolute error / Actual measurement
EG 0.05 / 8.3 = ±0.006
Percentage error?
- The Percentage Error is the Relative Error shown as a percentage
- Absolute error / actual measurement x100
EG 0.05 / 8.3 x100 = ±0.6%
COMBINING ERRORS RULES
- When you add / subtract 2 numbers with errors?
- When you multiply divide 2 numbers with errors?
- When values are raised to a power / fraction?
- Rule 1: When you add / subtract 2 numbers with errors = add the absolute errors
- Rule 2: When values are multiplied / divided the percentage errors are ADDED
- Rule 3: When values are raised to a power OR
fraction e.g. y^2 the percentage errors are
MULTIPLIED by the power
Data analysis
Graphs
- X and Y axis?
S.A.L.T ?
- Independent variables = X axis (Horizontal) [variable being changed]
- Dependent variables = Y axis (Vertical) [variable affected + measured]
- Axes need labels in the form: Quantity/unit
e.g. Time/minutes. distance/cm. volume/cm³
S- Scale
A- Axis
L- Labels
T- Title
- draw full triangles on tangent for gradient
Rates of change?
- The gradient of a graph plotted against time will be the “rate of change” of the dependent variable
- eg how much its value
(volume, temperature- this is y) changes per second, minute, hour etc
relationships between variables
Relationships can be…
➢ Linear
➢ Non-linear
➢Directly proportional
➢Inversely proportional
➢ Linear: The two variables give a straight line graph.
➢ Non-linear: The rate of increase in one variable = not the same as the rate of increase in the other variable = curved line on a graph
➢Directly proportional: as one increases, the other increases by the same percentage [y ∝ x or
y=mx….straight + ALWAYS passes by the origin]
➢Inversely proportional: when one value decreases at the same rate that the other increases.
[x ∝ 1/y or y =𝟏/𝒙]
How to convert Inversely proportional graphs into straight line graphs
for each value in the ‘Y’ axis = do 1÷ Y for each of them = plot these new values [use same x values]
1 / y
