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

lengthin. inchft Footmi mile

mass slug slugforce lb pound

time s second

thermodynamic temperature F Fahrenheit degree

Common Items: Size Comparison

Two sheets of paper

Human hair Diameter of paper clip

0.2 mm. 0.1 mm 0.8 mm

U S

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Syst

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Recording Measurements

• Measurements must always include units• Always errors in measurements

– measurements are the best “estimate” of a quantity• A measurement is only good if you are know that

it is reasonable close to the actual quantity• It is important to indicate the accuracy and

precision of your measurements• Scientists and engineers use significant digits to

make the accuracy and precision of measurements clear

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

High PrecisionLow Accuracy

High AccuracyHigh Precision

Recording Measurements

• Ideally, a measurement device is both accurate and precise

• Accuracy depends on calibration to a standard• Precision depends on the characteristics and/or

capabilities of the measuring device and its use• Use significant digits to indicate the accuracy

and precision of experimental results– Record only to the precision to which you and your

measuring device can measure

Significant Digits

• Accepted practice in science is to indicate accuracy and/or precision of measurement

• Significant digits are digits in a decimal number that carry meaning contributing to the precision or accuracy 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

• Manufacturers of equipment usually indicate the accuracy and precision of the instrument

• 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 an 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 common a 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

 

 

Is 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• Record fraction measurements to the

nearest 1/32 inch.

• Record decimal equivalent to the nearest hundredths of an inch.

2 532

in.

2.16 in.

Your Turn

Record each measurement in fractional and decimal inches.