Measurement. Name: Slot: Essential Math 12 Mr. Morin. Accuracy, Precision and Uncertainty Tolerance

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1 Measurement Essential Math 12 Mr. Morin Name: Slot: Accuracy, Precision and Uncertainty Tolerance 1

Accuracy, Precision, and Uncertainty Accuracy The measurement is considered accurate if it is taken correctly, recorded correctly, and communicated correctly.

2 Accuracy, Precision, and Uncertainty Accuracy The measurement is considered accurate if it is taken correctly, recorded correctly, and communicated correctly. If care is taken so that measurement is correct. if it is easily understood and reproduced. Precision Precision is the smallest division of measuring device. The precision of a measurement differs from device to device. Uncertainty Uncertainty is directly related to precision. margin of error when reading measurement. 1 2 of the precision. Example 1 Ryan is a carpenter and measures a door as 7 x 3. a. How large is the door (describe in words)? b. Are there any potential issues with accuracy? 2

3 Example 2 Amy: How far of a drive is it from Winnipeg to Kenora? Rick: About a 2 hour drive. Are there any potential issues with accuracy in this brief conversation? Example 3 The above ruler is in centimetres. Identify the following, then write a brief description how you got your result. Precision Description of precision. Uncertainty Description of uncertainty. Example 4 3

The test tube pictured is used to measure water samples in a laboratory. The scale is in ml. It s Eric s first day on the job; he is nervous. He notes the water in the sample as 30L.

4 The test tube pictured is used to measure water samples in a laboratory. The scale is in ml. It s Eric s first day on the job; he is nervous. He notes the water in the sample as 30L. a) Identify the precision on the measuring device. b) Identify the uncertainty of the measuring device. c) Comment on the accuracy of Eric s measurement of 30L. Example 5 Jessica is organizing the RETSD track and field championship. In the 100m dash she must record the result in the form measurement ± uncertainty. The winner s time is recorded as Identify the 11.4 ± 0.05 sec Minimum time: Maximum time: 4

5 Example 6 Rachel measures a board with the following measuring tape. She accurately records the length as cm. a. What is meant by accurately? b. What is the precision of this measurement? c. What is the uncertainty of this measurement? d. Write the measurement and include it measurement ± uncertainty. e. Why is it important to write in the above form? Questions 1) Explain why you cannot rely on a measuring device to determine the exact length of an object. 2) Identify the precision and uncertainty. Precision: Uncertainty: 5

3) A manufacturer drills a hole into a board. An employee measures the diameter of the hole to be 4.37 mm. She knows that the device used to measure the hole has an uncertainty of 0.

(100m dash times are on the left; 10,000m race times are on the right.) 5) The length of a school s garden is measured using a stick that has been cut to 1 metre in length.

6 3) A manufacturer drills a hole into a board. An employee measures the diameter of the hole to be 4.37 mm. She knows that the device used to measure the hole has an uncertainty of 0.02 mm. Express the minimum and maximum diameters of the hole in mm. Minimum: Maximum: 4) Explain why a timer for a 100 m race would need to be more precise than a timer for a 10 km run. (100m dash times are on the left; 10,000m race times are on the right.) 5) The length of a school s garden is measured using a stick that has been cut to 1 metre in length. State the precision and uncertainty in the measurements made using the stick. Precision: Uncertainty: 6) Describe a measurement situation and explain why a certain degree of accuracy would be required. 6

7 7) A metre stick is divided into 100 centimetres. State the precision and uncertainty for the metre stick. 8) Gold is trading at $1 300 per ounce. Explain why a jeweller would want to be very accurate when weighing gold to make a ring. 9) A graduated cylinder is a measuring device used for liquids. Express the precision and uncertainty for the given graduated cylinder. Precision: Uncertainty: 10) State a measurement situation where a degree of precision would be required. Justify your answer. 11) State the precision and uncertainty Precision : Uncertainty: 7

8 12) An odometer is used to measure the distance a car travels. The trip odometer reads km. State the precision and uncertainty of the odometer. Precision: Uncertainty: 13) A metre stick is left outside in the sun and it expands. Explain how this will affect the stick s accuracy and precision. Tolerance 8

9 Examples 1) In order for a hex nut to function properly its interior diameter must be between a minimum of 1.5cm to a maximum of 1.7cm. a) Write in the four tolerance notations. b) Identify when each notation of tolerance is used. 2) A manufactured steel plate must have a length of 200 ± 2 mm. Identify the nominal value and tolerance. 9

10 3) A manufacturer makes screw cap for bottles with the diameters that have nominal value of 2.00 cm and tolerances of 0.01 cm. State the minimum and maximum diameter of a screw cap if the nominal value is the midpoint of the tolerance range. Minimum: Maximum: Questions 1) State the similarities between tolerance and uncertainty. State the differences. 2) Write the following into the four different tolerance notations 36.0 ± 0.5 nomial value +tolerance ± 1 nominal value 0 2 tolerance 0 nominal value tolerance maximum minimum Maximum value:17.5 Minimum value:

11 3) Identify industries where a certain degree of tolerance is required. Support your example with an explanation of how tolerance was required. 4) The tolerance for the diameter of a support beam can be describe in two ways or Identify the maximum and minimum of both notations Maximum: Maximum: Minimum: Minimum: c) Identify when is more useful. 0 d) Identify when is more useful. 5) The width of a door frame has a nominal value of 36 inches (which is halfway between the minimum and maximum value). The tolerance is 0.5 inches. State the minimum and maximum values of the width of the door frame. Maximum: Minimum: 11

12 6) An engineering drawing states that an electronic pin has the following length: 4.2 mm 4.0 Identify the nominal value and the tolerance. Nominal Value: Tolerance: 7) A steel manufacturer creates an item that must be 5 cm across with a tolerance of 0.2 cm ( ± 0.1 cm). The manufacturer writes the measurements of the item in the form a b 0 Identify the value of: a: b: 8) Dave wants to install three new cupboards in his bathroom. Each cupboard is 40 cm wide. He measured the space to be 120 cm wide. Explain why the cupboards may not fit using one of the following concepts: accuracy, tolerance, or uncertainty. 9) A company manufactures cylinders that must have a mass of 4.82 kg, within a tolerance of 0.24 kg. State the minimum mass. State the maximum mass. 12

13 10) A manufacturer creates ball bearings with diameters that have nominal values of 5 cm and tolerances of 0.02 cm. State the minimum and maximum diameter of a ball bearing if the nominal value is the midpoint of the tolerance range. Minimum: Maximum: 11) The width of a door frame has a nominal value of 36 inches (which is halfway between the minimum and maximum value). The tolerance is 0.5 inches. State the minimum and maximum values of the width of the door frame. 12) A welding company has determined that the desired length of a steel arm is 2cm ± 0.5cm. The tolerance is given in the form 0 nominal value tolerance State the nominal value and tolerance. Nominal Value: Tolerance: 13

Measurement instruments and procedures

Measurement instruments and procedures To study and understand Natural Science we have to do some work in the laboratory. To carry this out we need to use a range of lab material. In this presentation we will see the essential materials and