Unit 11: Measurement and Data Processing ; Topic 11.1 & 11.2 Uncertainty & Error

Question 1

Qualitative data is…

Answer 1

non-numerical data obtained from an experiment. These will be observations made during an experiment.

Question 2

Quantitative data is…

Answer 2

numerical data

Question 3

why do random errors arise?

Answer 3

due to the limitations of the measuring apparatus.

Question 4

what else is random errors called?

Answer 4

human error

Question 5

how are random errors determined?

Answer 5

it is determined by the experimenter’s skill or ability to perform the experiment and read scientific measurements.

Question 6

what should all measurements be quoted with?

Answer 6

an uncertianty

Question 7

what does the uncertainty indicate?

Answer 7

the size of the random error

Question 8

what is an Analogue apparatus?

Answer 8

mechanical devices that indicate the magnitude of the quantity in the form of the pointer movement

Question 9

when using an Analogue apparatus the uncertainty on a measurement is half of the what?

Answer 9

the smallest division that you take a reading to.

Question 10

what is a Digital Instrument?

Answer 10

The instrument which represents the measured value in the form of the digital number

Question 11

when using a digital instrument the uncertainty on a measurement is quoted as…

Answer 11

± the smallest division

Question 12

what is an example of uncertainty with a reading taken with a 2-decimal place electronic balance? (digital instrument)

Answer 12

2.46 ± 0.01g.

Question 13

if a voltmeter has an analogue scale and the smallest scale division is 1 volt, what is the uncertainty from reading this scale?

Answer 13

± 0.5 volts.

Question 14

if a voltmeter has a digital scale that reads 13.8, What is the uncertainty from reading this scale? and how was that derived?

Answer 14

The uncertainty from reading this scale is ± 0.1 volts. This is because the least significant digit is the 8.

Question 15

what does the effects of random uncertainties mean?

Answer 15

The effects of random uncertainties should mean that the measurements taken will be distributed on either side of the mean.

Question 16

can random uncertainties be completely eliminated?

Answer 16

The random uncertainties can never be completely eliminated but the effect of random uncertainties can be reduced.

Question 17

How can you reduce the effect of the random uncertainties?

Answer 17

by repeating the measurements more often.

Question 18

what is a Systematic error?

Answer 18

Systematic errors are errors that affect the accuracy of a measurement.

Question 19

how can a systematic error be introduced into an experiment?

Answer 19

A systematic error can be introduced into an experiment due to the apparatus used or the procedure.

Question 20

are systematic errors are always in the same direction?

Answer 20

yes

Question 21

how can the presence of systematic errors be identified?

Answer 21

by comparison with accepted literature values for quantities.

Question 22

what do we use to compare the experimental value with the accepted literature value?

Answer 22

percentage error

Question 23

what is the formula for percentage error?

Answer 23

= (experimental value – accepted value/accepted value) x 100

Question 24

how do you know if the experiment involves some systematic errors?

Answer 24

If the percentage error is greater than the percentage uncertainty due to random errors

Question 25

what happens if the percentage error is smaller than the percentage uncertainty

Answer 25

any deviation from the literature value can be explained in terms of random errors, that is, the limitations of the measuring apparatus.

Question 26

what does precision relate to?

Answer 26

reproducibility of results, meaning that multiple measurements give nearly identical values.

Question 27

what does high precision mean?

Answer 27

High precision means that repeat values are close together and close to the mean.

Question 28

what does accuracy refer to?

Answer 28

how close a measurement is to the actual value of a particular quantity.

Question 29

what is low accuracy due to?

Answer 29

Low accuracy is due to systematic errors within the experimental procedure.

Question 30

how are random errors characterized in terms of precision and accuracy?

Answer 30

Random errors are characterized by high accuracy and low precision

Question 31

how are systematic errors characterized in terms of precision and accuracy?

Answer 31

Systematic errors are characterized by high precision but low accuracy.

Question 32

The uncertainty is usually quoted to how many significant figures?

Answer 32

one

Question 33

how should the measurement be stated?

Answer 33

the measurement should be stated so that the uncertainty is in the last significant figure – no figures should be quoted after the uncertainty.

Question 34

Consider a value of 1.735 ± 0.1 obtained from an equation, The uncertainty is in this decimal place, so no figures should be quoted beyond it. This quantity should then be quoted as...

Answer 34

1.7± 0.1.

Question 35

what are the significant digits rules?

Answer 35

- All non-zero digits are significant. - “Captive” zeros (zeros between non-zero digits) are significant. - Leading zeros (zeros on the left) are never significant. - Trailing zeros… A). Are not significant if they are place holders(left of a decimal) B). Are significant if they indicate a measurement (right of a decimal) - Exact numbers (counting numbers) have unlimited significant digits.

Question 36

what are the rules for rounding off?

Answer 36

- If the digit to be removed: A) is less than 5 the preceding digits stays the same. B) is 5 or greater, the preceding number is increased by 1.

Question 37

how do you add and subtract significant digits?

Answer 37

- Add up the digits by columns. - Round off the final answer to the same number of decimal places as the least precise number.

Question 38

how do you multiply and divide significant digits?

Answer 38

- Multiply the values as normal. - Round off the final answer to the same number of significant digits as the least precise number.

Question 39

Uncertainty's may be reported in what 2 forms?

Answer 39

absolute value, eg. 1.23 ± 0.02m or as a percentage value, eg. 1.23m ± 2%

Question 40

out of absolute and relative uncertainties which best fits with the statement "for any measuring device is the same for each measurement."

Answer 40

Absolute Uncertainty

Question 41

Absolute Uncertainty =

Answer 41

% Uncertainty / 100 x Value

Question 42

For Example: if the final value of calculation is 23.27 ± 1%, the Absolute Uncertainty = 1/100 x 23.27 = 0.2 Therefore, final answer is...

Answer 42

23.27 ± 0.2

Question 43

Percentage / Relative Uncertainty is the measure of the uncertainty with respect to what?

Answer 43

measure of the uncertainty with respect to the magnitude of the measurement.

Question 44

how is Percentage / Relative Uncertainty expressed?

Answer 44

It is expressed as a % with 1 or 2 s.f

Question 45

Percentage Uncertainty =

Answer 45

= Absolute uncertainty / Value x 100

Question 46

When adding or subtracting measurements, we add the what uncertainty?

Answer 46

absolute

Question 47

When multiplying or dividing measurements we add the what uncertainty?

Answer 47

relative/percentage

Question 48

Eg. Calculate the absolute uncertainty when 9.78 ± 0.04 is divided by 3.349 ± 0.005 and quote the final answer to an appropriate number of significant figures.

Answer 48

Answer = 2.92 ± 0.02

Question 49

Graphs are used extensively in science to show the relationship between two variables. Graphs may be either...

Answer 49

Sketched graphs, or Drawn graphs

Question 50

sketched graphs are where...

Answer 50

the axes are labelled but there is no scale.

Question 51

drawn graphs are where...

Answer 51

the axes are labeled and have scales.

Question 52

what is the independent Variable?

Answer 52

What is changed in an experiment – what is being investigated.

Question 53

what is the dependent Variable?

Answer 53

What is measured in an experiment.

Question 54

Fill in the blanks: The line of best fit must be a -- line and pass through the -- for a -- relationship.

Answer 54

The line of best fit must be straight line and pass through the origin for a proportional relationship.

Question 55

The gradient (slope) gives us an idea of what?

Answer 55

how much one quantity (the dependent variable) is affected by another quantity (the independent variable).

Question 56

what happens If the gradient is large?

Answer 56

then a small change in the independent variable has a large effect on the dependent variable.

Question 57

Gradient=

Answer 57

= Change in Y / change in X

Question 58

The units of the gradient are obtained by...

Answer 58

dividing the units of the quantity on the y-axis by the units of the quantity on the x-axis.

Question 59

what do you do to determine the gradient of a curve?

Answer 59

For a curve draw a tangent and determine the gradient of the tangent.