US Customary Measurement System

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

Measurement Symbol Unit

length

in. inch

ft foot

mi mile

mass slug slug

force 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.

F=¼D=.26

F=31/32D=.97

F=1-3/4D=1.76

F=2-13/32D=2.41

F=3-1/32 D=3.03