US Customary Measurement System

1. US Customary Measurement System 3.1 Linear Measurement US and SI Standards

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

4. Recording Measurements • A measurement always includes units • A measurement always includes error • A measurement is the best estimate of a quantity • Scientists and engineers often use significant digits to indicate the uncertainty of a measurement • Indicate the accuracy and precision of your measurement

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 Low Accuracy High Precision High Accuracy High Precision

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

7. Significant Digits • Accepted practice in science is to indicate uncertainty of measurement • Significant digits are digits in a decimal number that carry meaning contributing to the uncertainty 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 • 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 the 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. Your turn • You have 5 minutes to see who gets the highest score on ‘The Ruler Game’ • http://www.rickyspears.com/rulergame/ • Set units to 1/16”

18. SI Measurement System

19. Why are measurement units important? • September 30, 1999Web posted at: 1:46 p.m. EDT (1746 GMT) • (CNN) -- NASA lost a $125 million Mars orbiter because one engineering team used metric units while another used English units for a key spacecraft operation, according to a review finding released Thursday.

20. The International System of Units (SI) • The International System of Units (SI) is a system of units of measurement consisting of seven base units • Mostly widely used system of measurement • The United States is the only industrialized nation that has not adopted the SI system

21. The International System of Units • Often referred to as the metric scale • Prefixes indicate an integer power of 10

22. Common Items: Size Comparison

23. Recording Measurements • A measurement always includes a value • A measurement always includes units • A measurement always involves uncertainty • A measurement is the best estimate of a quantity

24. Significant Digits Scientists and engineers often use significant digits to indicate the uncertainty of a measurement • Significant digits are digits in a decimal number that carry meaning indicating the certainty of the value • All digits you record for a measurement are considered significant • Include all certain digits in a measurement and one uncertain or estimated digit

25. Significant Digits • General Rules • Digital Instruments – Read and record all digits, 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

26. Metric Scale • A typical metric scale often includes a30+ centimeter graduated scale • Each centimeter is graduated into 10 millimeters

27. The Millimeter • The millimeter is the smallest increment found on a typical metric scale 1 mm

28. The Millimeter • The next larger marking on a metric scale shows 5 millimeters 5 mm

29. The Millimeter • Largest markings on a metric scale represent centimeters (cm) • These are the only marks that are actually numbered 1 cm = 10 mm

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

31. Measurement: Using a Decimal Scale • How long is the rectangle?

32. Practice Worksheet 3.1a • On problem 8, measure each of the values in US (to the nearest 1/16”) and SI (to the nearest 0.01 cm)