Precision

How can we achieve the most precise readings?

Record data to the correct number of precision according to the type of recording instrument

Which is more precise? 9.1cm or 9.10cm

9.10cm

What is the definition of precision of an instrument?

Precision refers to how exactly a single measurement is taken

What is accuracy of a measurement?

Accuracy refers to how close the reading is to the “true” value measured

Why would a measurement be accurate but not precise?

Limitations of the instrument

Why would a measurement be precise but not accurate?

Systematic/random errors

How can we minimise these limitations/errors?

Repeat experiment and take the average of the results to minimise human errors

Use different set of instruments to reduce systematic errors.

Scrutinise the skills used by the experimenter in making measurements to minimise human error

RUS

What are the two types of errors?

Systematic errors and random errors

Why do systematic errors occur?

1. Something is wrong with the measuring instrument.

e.g zero error. A zero error is subtracted from the instrument reading

2. The instrument is read wrongly consistently by the person performing the experiment.

Why do random errors occur?

Due to unpredictable environmental or human factors

So what do random errors do to the measured value?

Make them less accurate and precise.

How can we account for random errors?

1. Repeating experiment and get the average of several readings for a single set of data

2. Getting several sets of data, plotting a graph and drawing line of best fit.

What do we do when an instruments has a zero error?

This is a systematic error. It must be subtracted from the instrument reading in order to obtain the actual reading. (E.g. TARE on electronic balance)

How should we calculate precision?

Half of the smallest division (generally)

Smallest division (e.g. meter rulers, protractors, electronic balances, stopwatches)

So what are the instruments that are read to half the smallest division? And what is the precision of these instruments? (divisions of these instruments are larger)

Measuring cylinder (0.1cm³, to 1 d.p.)

Thermometer (0.1°C Digital, 0.5°C Lab)

Spring Balance (0.5N but to 1 d.p.)

Ammeter (0.05A, to 2 d.p.)

Voltmeter (0.01V to 2 d.p.)

So what instruments are read to the smallest division?

Meter ruler (1mm, 0.1cm, 0.001m. Look at question paper for the units to be used)

Protractor (1°, to nearest whole number)

Electronic balance (0.01g, to 2 d.p.)

SPECIAL CASE:

Stopwatch (0.1s OR 0.01s, record in 1 d.p. in s not 2d.p. due to human reaction time error of 0.3s. But if timing is very short, record 0.01s, 2d.p.)

But why do we use the smallest division for the precision of a protractor?

Due to the error of +-0.5 of the two lines.

How should we make a table?

Heading should have units reflected, so data values do not require units

Unit in the heading should be “/cm” (e.g.) and not “(cm)”

Independent Variable column uses values with EQUAL and EVEN increments

The recorded data should reflect the precision of the instrument (e.g. 1d.p. in cm shows that a metre ruler is used.)

Calculated values should follow consistent number of decimal places

1 d.p. in s shows what instrument is used?

Digital stopwatch used by manual control of a human, who has a reaction time of 0.3s.

(human error must be accounted even if stopwatch displays 2 d.p. readings)

What should we do to the data when it is added or subtracted?

Final answer should be rounded off to the least decimal places

If data is multiplied or divided, what should we do?

Final answer should be rounded off to the least significant figure

When calculating using measured data that involves all + / -, x, /, (e.g. finding gradient), what should we do?

Calculated data should be rounded off to 2 or 3 s.f.

What should we do to data when we find average?

Calculated answer should follow the same precision as the measuring instrument.

Calculated value should NOT be more accurate than the least accurate measured data.

How can we improve accuracy for measurements that is too small?

Measure a few together and find the average.

If we are finding the density of a marble, we take the mass of 5 marbles and divide volume of the 5 marbles, and not find the density of individual marbles.

How should we draw graphs?

S → Scale

T → Title

A → Axis

P → Points

L → Line

Explain Scale

e.g. Y axis 1cm rep 2 units,

X axis 2cm rep 1 unit.

Choose a scale that the plots are well spread out on the ENTIRE graph paper.

DO NOT USE ODD SCALES like 3cm rep 1 unit, or 1cm rep 7 units.

Mark the axes clearly with equal intervals and label the markings in the SAME d.p. according to table of data.

Explain Title

Titled as:

Graph of Y/unit against X/unit.

Explain AXES

Labeled clearly with the symbol and units (e.g. L/cm)

DO NOT LABEL L(cm) with brackets

Explain Points

PLOT the points clearly with a CROSS X

Explain Line

Draw the best-fit LINE

What are the possible conclusions of a linear graph?

e.g.

L/cm is DIRECTLY PROPORTIONAL to V/V (pass thru origin)

L/cm is LINEARLY RELATED to V/V (no pass thru origin)

L/cm is LINEARLY RELATED to V/V WITH A NEGATIVE CONSTANT

How do we calculate the gradient?

(y2 - y1)/(x2 - x1) (lowest s.f. value of the number used)

What are the errors that can affect the period of oscillation and the step(s) that you can take to reduce these errors?

1. Human reaction time when starting and stopping the stopwatch introduces random error. Repeat the experiment a few times and calculate the average to reduce the random error

2. The pendulum may swing in an irregular manner or elliptical motion, altering the period slightly. Release the bob gently without a push, ensuring it swings in one vertical plane.