US Measurement System © 2012 Project Lead The Way, Inc. - PowerPoint Presentation

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USMeasurement System

© 2012 Project Lead The Way, Inc.

Introduction to Engineering Design

The U S Customary SystemSystem of measurement used in the United States Similar to the British Imperial System of Measurement, but not identicalCommon U S Customary UnitsMeasurement

Symbol

Unitlengthin.

inch

ft

foot

mi

mile

mass

slug

slug

force

lb

pound

time

s

second

thermodynamic

temperature

F

Fahrenheit degree

Common Items: Size Comparison

Recording MeasurementsA measurement always includes unitsA measurement always includes errorA measurement is the best estimate of a quantityScientists and engineers often use significant digits to indicate the uncertainty of a measurementIndicate the accuracy and precision of your measurement

Precision and AccuracyPrecision (repeatability) = The degree to which repeated measurements show the same resultAccuracy = 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 MeasurementsIdeally, a measurement device is both accurate and preciseAccuracy is dependent on calibration to a standardPrecision is dependent on the characteristics and/or capabilities of the measuring device and its useRecord only to the precision to which you and your measuring device can measure

Significant DigitsAccepted practice in science is to indicate uncertainty of measurementSignificant digits are digits in a decimal number that carry meaning contributing to the uncertainty of the quantityThe digits you record for a measurement are considered significantInclude all certain digits in a measurement and one uncertain digitNote: Fractions are “fuzzy” numbers in which significant digits are not directly indicated

Recording MeasurementsGeneral RulesDigital Instruments: Read and record all the numbers, including zeros after the decimal point, exactly as displayedDecimal Scaled Instruments: Record all digits that you can certainly determine from the scale markings and estimate one more digitPreferred over fractional scaled instrumentsFractional Scaled Instruments: Need special consideration

Fractional Length MeasurementA typical ruler providesA 12 inch graduated scale in US Customary unitsEach inch is graduated into smaller divisions, typically 1/16” increments

The InchThe 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 InchEach 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 InchHalf 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 InchHalf of a quarter = 1/8 inch

1/8

3/8

7/8

5/8

The InchHalf 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 ScaleHow long is the rectangle?Let’s look a little closer

Measurement: Using a Fractional ScaleHow long is the rectangle?What fraction of an inch does this mark represent?

1/2

1/4

1/8

3/16

Measurement: Using a Fractional ScaleHow 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 ScaleHow 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 ScaleHow long is the rectangle?Remember the General RuleFractional Scaled Instruments require special consideration  

Are

6 significant digits appropriate???1/16 in. = .0625 in.

Your TurnRecord each measurement in fractional and decimal inches.