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Errors & Uncertainties | Physics for Grade 10 PDF Download

Random & Systematic Errors

  • Measurements of quantities are made with the aim of finding the true value of that quantity
  • In reality, it is impossible to obtain the true value of any quantity, there will always be a degree of uncertainty
  • The uncertainty is an estimate of the difference between a measurement reading and the true value
  • Random and systematic errors are two types of measurement errors which lead to uncertainty

Random error

  • Random errors cause unpredictable fluctuations in an instrument’s readings as a result of uncontrollable factors, such as environmental conditions
  • This affects the precision of the measurements taken, causing a wider spread of results about the mean value
  • To reduce random error: repeat measurements several times and calculate an average from them

Systematic error

  • Systematic errors arise from the use of faulty instruments used or from flaws in the experimental method
  • This type of error is repeated every time the instrument is used or the method is followed, which affects the accuracy of all readings obtained
  • To reduce systematic errors: instruments should be recalibrated or the technique being used should be corrected or adjusted

Errors & Uncertainties | Physics for Grade 10

Representing precision and accuracy on a graph

Zero error

  • This is a type of systematic error which occurs when an instrument gives a reading when the true reading is zero
  • This introduces a fixed error into readings which must be accounted for when the results are recorded

Precision & Accuracy

  • Precision of a measurement: this is how close the measured values are to each other; if a measurement is repeated several times, then they can be described as precise when the values are very similar to, or the same as, each other
  • The precision of a measurement is reflected in the values recorded - measurements to a greater number of decimal places are said to be more precise than those to a whole number
  • Accuracy: this is how close a measured value is to the true value; the accuracy can be increased by repeating measurements and finding a mean average Errors & Uncertainties | Physics for Grade 10

The difference between precise and accurate results

Calculating Uncertainty

  • There is always a degree of uncertainty when measurements are taken; the uncertainty can be thought of as the difference between the actual reading taken (caused by the equipment or techniques used) and the true value
  • Uncertainties are not the same as errors
    • Errors can be thought of as issues with equipment or methodology that cause a reading to be different from the true value
    • The uncertainty is a range of values around a measurement within which the true value is expected to lie, and is an estimate
  • For example, if the true value of the mass of a box is 950 g, but a systematic error with a balance gives an actual reading of 952 g, the uncertainty is ±2 g
  • These uncertainties can be represented in a number of ways:
    • Absolute Uncertainty: where uncertainty is given as a fixed quantity
    • Fractional Uncertainty: where uncertainty is given as a fraction of the measurement
    • Percentage Uncertainty: where uncertainty is given as a percentage of the measurement
      Errors & Uncertainties | Physics for Grade 10
  • To find uncertainties in different situations:
  • The uncertainty in a reading: ± half the smallest division
  • The uncertainty in a measurement: at least ±1 smallest division
  • The uncertainty in repeated data: half the range i.e. ± ½ (largest - smallest value)
  • The uncertainty in digital readings: ± the last significant digit unless otherwise quoted

Errors & Uncertainties | Physics for Grade 10

How to calculate absolute, fractional and percentage uncertainty

Combining Uncertainties

  • The rules to follow
  • Adding / subtracting data – add the absolute uncertainties

Errors & Uncertainties | Physics for Grade 10

  • Multiplying / dividing data – add the percentage uncertainties

Errors & Uncertainties | Physics for Grade 10

  • Raising to a power – multiply the uncertainty by the power

Errors & Uncertainties | Physics for Grade 10

Measurement Techniques

  • Common instruments used in Physics are:
    • Metre rules - to measure distance and length
    • Balances - to measure mass
    • Protractors - to measure angles
    • Stopwatches - to measure time
    • Ammeters - to measure current
    • Voltmeters - to measure potential difference
  • More complicated instruments such as the micrometer screw gauge and Vernier calipers can be used to more accurately measure length

Errors & Uncertainties | Physics for Grade 10


  • When using measuring instruments like these you need to ensure that you are fully aware of what each division on a scale represents
    • This is known as the resolution
  • The resolution is the smallest change in the physical quantity being measured that results in a change in the reading given by the measuring instrument
  • The smaller the change that can be measured by the instrument, the greater the degree of resolution
  • For example, a standard mercury thermometer has a resolution of 1°C whereas a typical digital thermometer will have a resolution of 0.1°C
    • The digital thermometer has a higher resolution than the mercury thermometer

 Measuring Instruments Table

Errors & Uncertainties | Physics for Grade 10

Micrometer Screw Gauge

  • A micrometer, or a micrometer screw gauge, is a tool used for measuring small widths, thicknesses or diameters
    • For example, the diameter of a copper wire
  • It has a resolution of 0.01 mm
  • The micrometer is made up of two scales:
    • The main scale - this is on the sleeve (sometimes called the barrel)
    • The thimble scale - this is a rotating scale on the thimble
  • The spindle and anvil are closed around the object being measured by rotating the ratchet
    • This should be tight enough so the object does not fall out but not so tight that is deformed
    • Never tighten the spindle using the barrel, only using the ratchet. This will reduce the chances of overtightening and zero errors
  • The value measured from the micrometer is read where the thimble scale aligns with the main scale
    • This should always be recorded to 2 decimal places (eg. 1.40 mm not just 1.4 mm)

Errors & Uncertainties | Physics for Grade 10

How to operate a micrometer

Vernier Calipers

  • Vernier calipers are another distance measuring tool that uses a sliding vernier scale
    • They can also be used to measure diameters and thicknesses, just like the micrometer
    • However, they can also measure the length of small objects such as a screw or the depth of a hole
  • Vernier calipers generally have a resolution of 0.1 mm, however, some are as small as 0.02 mm - 0.05 mm
  • The calipers are made up of two scales:
    • The main scale
    • The vernier scale
  • The two upper or lower jaws are clamped around the object
    • The sliding vernier scale will follow this and can be held in place using the locking screw
  • The value measured from the caliper is read when the vernier scale aligns with the main scale
    • This should always be recorded to at least 1 decimal place (eg. 12.1 mm not just 12 mm)

Errors & Uncertainties | Physics for Grade 10

The vernier caliper reading is read when the vernier scale aligns with the main scale

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