The U S Customary Measurement System • System of measurement used in the United States • Similar to the British Imperial System of Measurement, but not identical
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
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
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
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
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
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
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.
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
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
The Inch • Half of a quarter = 1/8 inch 7/8 1/8 3/8 5/8
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
Measurement: Using a Fractional Scale • How long is the rectangle? • Let’s look a little closer
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
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
Measurement: Using a Fractional Scale • How do we determine that 5/32 is midway between 1/8 and 3/16? • Convert each fraction to a common denominator: 32 5 Find the average of the two measurements
Recording a Measurement: Using a Fractional Scale • How long is the rectangle? • Remember the General Rule • Fractional Scaled Instruments require special consideration • Are 6 significant digits appropriate??? • 1/16 in. = .0625 in.
Recording a Measurement: Using a Fractional Scale • For the standard ruler marked in 1/16 inch increments (least count = 1/16 in.) • Record fraction measurements to the nearest 1/32 inch • Record decimal equivalent to the nearest hundredths of an inch • Record with your data • The least count of the scale (1/16 in.) • The increment to which measurements are estimated (nearest 1/32 in.) 5 32 2 in. 2.16 in.
Your Turn Record each measurement in fractional and decimal inches.