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US Customary Measurement System

US Customary Measurement System. The U S Customary System. System of measurement used in the United States Similar to the British Imperial System of Measurement, but not identical. Common Items: Size Comparison. U S Customary System. S I. Recording Measurements.

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US Customary Measurement System

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  1. US Customary Measurement System

  2. The U S Customary System • System of measurement used in the United States • Similar to the British Imperial System of Measurement, but not identical

  3. Common Items: Size Comparison U S Customary System S I

  4. Recording Measurements • Measurements must always include units • Always errors in measurements • measurements are the best “estimate” of a quantity • A measurement is only good if you are know that it is reasonable close to the actual quantity • It is important to indicate the accuracy and precision of your measurements • Scientists and engineers use significant digits to make the accuracy and precision of measurements clear

  5. Precision and Accuracy • Precision (repeatability) = the degree to which repeated measurements show the same result • Accuracy = the degree of closeness of measurements of a quantity to the actual (or accepted) value High Accuracy Low Precision High Precision Low Accuracy High Accuracy High Precision

  6. Recording Measurements • Ideally, a measurement device is both accurate and precise • Accuracy depends on calibration to a standard • Precision depends on the characteristics and/or capabilities of the measuring device and its use • Use significant digits to indicate the accuracy and precision of experimental results • Record only to the precision to which you and your measuring device can measure

  7. Significant Digits • Accepted practice in science is to indicate accuracy and/or precision of measurement • Significant digits are digits in a decimal number that carry meaning contributing to the precision or accuracy of the quantity • The digits you record for a measurement are considered significant • Include all certain digits in a measurement and one uncertain digit • Note: fractions are “fuzzy” numbers in which significant digits are not directly indicated

  8. Recording Measurements • Manufacturers of equipment usually indicate the accuracy and precision of the instrument • General Rules • Digital Instruments – read and record all the numbers, including zeros after the decimal point, exactly as displayed • Decimal Scaled Instruments – record all digits that you can certainly determine from the scale markings and estimate one more digit • Preferred over fractional scaled instruments • Fractional Scaled Instruments – need special consideration

  9. Fractional Length Measurement • A typical ruler provides • A 12 inch graduated scale in US Customary units • Each inch is graduated into smaller divisions, typically 1/16” increments

  10. The Inch • The divisions on an U S Customary units scale are easily identified by different sized markings. The largest markings on the scale identify the inch.

  11. The Inch • Each subsequently shorter tick mark indicates half of the distance between next longer tick marks • For example the next smaller tick mark indicates half of an inch = ½ inch 1/2

  12. The Inch • Half of a half = ¼ inch. An English scale shows ¼ inch and ¾ inch marks. • All fractions must be reduced to lowest terms 1/4 3/4

  13. The Inch • Half of a quarter = 1/8 inch 7/8 1/8 3/8 5/8

  14. The Inch • Half of an eighth = 1/16 inch 1/16 9/16 5/16 13/16 3/16 7/16 11/16 15/16

  15. Measurement: Using a Fractional Scale • How long is the rectangle? • Let’s look a little closer

  16. Measurement: Using a Fractional Scale • How long is the rectangle? • What fraction of an inch does this mark represent? 3/16 1/4 1/2 1/8

  17. Measurement: Using a Fractional Scale • How long is the rectangle? What is the midpoint of 2 1/8 and 2 3/16? 5/32 3/16 1/8

  18. Measurement: Using a Fractional Scale • How do we determine that 5/32 is midway between 1/8 and 3/16? • Convert each fraction to common a denominator: 32 5 Find the average of the two measurements

  19. Recording a Measurement: Using a Fractional Scale • How long is the rectangle? • Remember the General Rule • Fractional Scaled Instruments – require special consideration • Is 6 significant digits appropriate??? • 1/16 in. = .0625 in.

  20. Recording a Measurement: Using a Fractional Scale • For the standard ruler marked in 1/16 inch increments • Record fraction measurements to the nearest 1/32 inch. • Record decimal equivalent to the nearest hundredths of an inch. 5 32 2 in. 2.16 in.

  21. Your Turn Record each measurement in fractional and decimal inches.

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