US Customary Measurement System © 2012 Project Lead The Way, Inc.Introduction to Engineering Design

What is the length of the following?

Label the increments on an inch

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 U S Customary Units MeasurementSymbolUnit length in.inch ftfoot mimile massslug forcelbpound timessecond thermodynamic temperature FFahrenheit degree

Common Items: Size Comparison

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. 1/43/4

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

The Inch Half of an eighth = 1/16 inch 1/16 3/16 5/16 13/16 7/16 11/16 9/16 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? 1/21/4 1/8 3/16

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

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.) in in.

Label the increments on an inch

Reading an inch ruler:

What is the length of the following? 7.41 in.

Your Turn Record each measurement in fractional and decimal inches.