US Customary Measurement System
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Transcript of US Customary Measurement System
US Customary Measurement System
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
Common U S Customary Units
Measurement Symbol Unit
lengthin. inchft footmi mile
mass slug slugforce lb pound
time s second
thermodynamic temperature F Fahrenheit 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 AccuracyLow Precision
Low AccuracyHigh Precision
High AccuracyHigh 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
1/8 3/8 7/85/8
The Inch
• Half of an eighth = 1/16 inch
1/163/16
5/16 13/167/16 11/16
9/1615/16
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
5Find 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.)
2 532
in.
2.16 in.
Your Turn
Record each measurement in fractional and decimal inches.