Unit B: Measurement

Practice


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  1. Hamal has two beakers available to measure 1 500 mL of water to boil spaghetti. One of the beakers has a maximum reading of 100 mL. The water can be measured in increments of 10 mL. The second beaker has a maximum reading of 300 mL. The water can be measured in increments of 25 mL.






    1. State the precision and uncertainty of each beaker.
    2. If Hamal fills each beaker to 75 mL, what volume of water could be in each beaker?
    3. Which beaker is more suitable to use to fill his pot with 1 500 mL of water to boil spaghetti?

  1. Erica measures the diameter of a wire (the true measurement of the diameter is 1.25683 mm) using different measuring devices. For each measuring tool, state the measurement that should be recorded and the measurement of uncertainty.






    1. ruler marked in centimetres
    2. tape measure marked in millimetres
    3. ruler marked in half-millimetres
    4. calliper, smallest increment is 0.01 mm
    5. micrometer, smallest increment is 0.002 mm

  2.  Juan recorded his weight on his bathroom scale as 176.5 lbs.





    Minutes later, Juan used a medical scale at the gym and recorded his weight as 174.8 lb.





    Juan then found a calibrated scale and measured his actual weight to be 176.1 lb. Answer the following questions by comparing the measurements from the bathroom and medical scales.

    1. What are the uncertainties for each scale?
    2. What is the range of measurement for both the bathroom scale and the medical scale?
    3. Which scale is more accurate: the bathroom scale or medical scale?
    4. Which scale is more precise: the bathroom scale or medical scale?
    5. How could the accuracy of the medical scale be improved?
Hamal has two beakers available to measure 1 500 mL of water to boil spaghetti. One of the beakers has a maximum reading of 100 mL. The water can be measured in increments of 10 mL. The second beaker has a maximum reading of 300 mL. The water can be measured in increments of 25 mL.






  1. State the precision and uncertainty of each beaker.
  2. If Hamal fills each beaker to 75 mL, what volume of water could be in each beaker?
  3. Which beaker is more suitable to use to fill his pot with 1 500 mL of water to boil spaghetti?

  1. The 100 mL beaker has a precision of 10 mL and an uncertainty of 5 mL. The 300 mL beaker has a precision of 25 mL and an uncertainty of 12.5 mL.
  2. In the 100 mL beaker, Hamal has 75 mL ± 5 mL or 70 mL to 80 mL of water. In the 300 mL beaker, Hamal has 75 mL ± 12.5 mL or 62.5 mL to 87.5 mL.
  3. Precision is not required when measuring water to boil spaghetti, so the 300 mL beaker should be used. Since the 300 mL beaker holds more water, it will take less time to fill the pot.
Erica measures the diameter of a wire (the true measurement of the diameter is 1.25683 mm) using different measuring devices. For each measuring tool, state the measurement that should be recorded and the measurement of uncertainty.






  1. ruler marked in centimetres
  2. tape measure marked in millimetres
  3. ruler marked in half-millimetres
  4. calliper, smallest increment is 0.01 mm
  5. micrometer, smallest increment is 0.002 mm
 
  1. The precision is 1 cm. The uncertainty of 0.05 cm is half of the precision. The measurement would be 0 cm ± 0.5 cm. The measurement is too small to record using a centimetre ruler.
  2. The precision is 1 mm. The uncertainty of 0.5 mm is half of the precision. The measurement would be 1 mm ± 0.5 mm.
  3. The precision is 0.5 mm. The uncertainty of 0.25 mm is half of the precision. The measurement would be 1.26 mm ± 0.005 mm.
  4. The precision is 0.01 mm. The uncertainty of 0.005 mm is half of the precision. The measurement would be 1.26 mm ± 0.005 mm.
  5. The precision is 0.002 mm. The uncertainty of 0.001 mm is half of the precision. The measurement would be 1.256 mm ± 0.001 mm.
Juan recorded his weight on his bathroom scale as 176.5 lb.





Minutes later, Juan used a medical scale at the gym and recorded his weight as 174.8 lb.





Juan then found a calibrated scale and measured his actual weight to be 176.1 lb. Answer the following questions by comparing the measurements from the bathroom and medical scales.

  1. What are the uncertaintes for each scale?
  2. What is the range of measurement for both the bathroom scale and the medical scale?
  3. Which scale is more accurate: the bathroom scale or medical scale?
  4. Which scale is more precise: the bathroom scale or medical scale?
  5. How could the accuracy of the medical scale be improved?

  1. The smallest increment on the bathroom scale is 1 lb, therefore the uncertainty is 0.5 lb.
    The smallest increment of the medical scale is 0.2 lb, therefore the uncertainty is 0.1 lb.
  2. The measurement on the bathroom scale is 176.5 lb ± 0.5 lb. The measurement range is 176.0 lb to 177.0 lb.
    The measurement on the medical scale is 174.8 lb ± 0.1 lb. The measurement range is 174.7 lb to 174.9 lb.
  3. The measurement of the bathroom scale is closer to the actual weight of 176.1 lb. The range of the medical scale does not include the actual weight of 176.1 lb.
  4. The medical scale has a higher precision since the smallest increment of measurement is 0.2 lb.
  5. The medical scale should be calibrated in order for it to produce weights that are closer to the actual (true) weight.