1: measurements and their errors

• How do you calculate the uncertainty when adding values?

  By adding the absolute uncertainties of the values being added.
• How do you calculate the uncertainty when subtracting values?

  By adding the absolute uncertainties of the values being subtracted.
• How do you calculate the uncertainty in repeat readings?

  the range of the values divided by 2
• When taking readings (when you don’t have to line up things therefore no zero error) what is the absolute uncertainty?

  Half the resolution (smallest division) of the instrument
• When taking measurements (when you do have to line things up therefore there is a zero error) what is the absolute uncertainity?

  The resolution (smallest division of the instrument) because there’s half of the resolution uncertainty at the beginning and end of the instrument
• How do you calculate the uncertainty with powers?

  Multiply the power by the percentage uncertainty
• How do you calculate the uncertainty in a gradient?

  • draw lines of best fit and of worst fit
  • find gradient of line of best fit and one line of worst fit
  • find the percentage uncertainty by calculating the difference between gradients divided by the gradient of the line of best fit and multiplying by 100
• What is the SI unit for mass?

  kilogram (kg)
• What is the SI unit for length?

  metre (m)
• What is the SI unit for time?

  second (s)
• What is theSI unit for amount of substance?

  mole (mol)
• What is the SI unit for temperature?

  kelvin (K)
• What is the SI unit for electric current?

  ampere (A)
• How do you convert from joules to electronvolts?

  divide by $1.6 \times 10^{-19}$
• How do you convert from electronvolts to joules?

  multiply by $1.6 \times 10^{-19}$
• How do you convert from joules to kilowatt-hours?

  divide by $3.6 \times 10^{6}$
• How do you convert from kilowatt-hours to joules?

  multiply by $3.6 \times 10^{6}$
• What is a random error?

  Unpredictable variation in an instrument’s reading as a result of uncontrollable factors such as environmental conditions. It affects the precision of the measurements taken which causes a wider spread of results about the mean value.
• How can you reduce random error?

  • repeats measurements several times and calculate a mean from them (this also allows anomalies to be identified)
  • use computers/data loggers/camera to reduce human error and enable smaller intervals
  • use appropriate equipment e.g. a micrometer had a higher resolution than a ruler
• What is a systematic error?

  Arise from the use of faulty instruments or from flaws in the experimental method. This type of error is repeated consistently every time the instrument is used it the method is followed, which affects the accuracy of all readings obtained. So it causes all results to be too high or too low by the same amount each time.
• How can you reduce systematic errors?

  • recalibrate the instruments by measuring a known value (e.g. weigh 1kg on a mass balance and if the reading is inaccurate then the systematic error is easily identified) or use different instruments
  • in radiation experiments correct for background radiation by measuring it beforehand and excluding it from final results
  • read the meniscus at eye level to reduce parallax error
  • use controls in experiments
• What is a zero error?

  A type of systematic error that occurs when an instrument gives a false reading when the true value of the measured quantity is zero. This introduces a fixed error into readings which must be accounted for when the results are recorded.
• What is repeatability?

  A measurement is repeatable if the original experimenter repeats the investigation using the same method and equipment and obtains the same results.
• What is reproducibility?

  A measurement is reproducible is the investigation is repeated by another person, or by using different equipment or techniques and the same results are obtained.
• What is precision?

  Precise measurements are ones in which there is very little spread about the mean value, in other words how close the measured values are to each other. If a measurement is repeated several times, it can be described as precise when the values are very similar to, or the same as, each other.
• What is accuracy?

  A measurement is considered accurate if it is close to the true value. The accuracy can then be increased by repeating measurements and finding a mean of the results. Repeating measurements also helps to identify anomalies that can be omitted from the final results.
• If a measurement is recorded to a greater values then what is it said to be more in comparison to values of a whole number?

  more precise
• What is resolution?

  The smallest change in the quantity being measured if a measuring instrument that gives a perceptible change in the reading. For example, the resolution of a wristwatch is 1s whereas the resolution of a digital stop-clock is typically 0.01s.
• What is resolution in relation to imaging?

  In imaging resolution can be described as the ability to see two structures as two separate structures rather than as one fuzzy entity.
• What is the power of ten value for peta (P)?

  $\times 10^{15}$
• What is the power of ten value for tera (T)?

  $\times 10 ^{12}$
• What is the power of ten value for giga (G)?

  $\times 10 ^{9}$
• What is the power of ten value for mega (M)?

  $\times 10 ^{6}$
• What is the power of ten value for kilo (k)?

  $\times 10 ^{3}$
• What is the power of ten value for centi (c)?

  $\times 10 ^{-2}$
• What is the power of ten value for milli (m)?

  $\times 10 ^{-3}$
• What is the power of ten value for micro (μ)?

  $\times 10 ^{-6}$
• What is the power of ten value for nano (n)?

  $\times 10 ^{-9}$
• What is the power of ten value for pico (p)?

  $\times 10 ^{-12}$
• What is the power of ten value for femto (f)?

  $\times 10 ^{-15}$