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
in.
inch
ft
Foot
mi
mile
mass
slug
slug
force
lb
pound
time
s
second
thermodynamic
temperature
F
Fahrenheit degree
length
Common Items: Size Comparison
Human hair
Diameter of paper
clip
0.2 mm.
0.1 mm
0.8 mm
SI
US
Customary
System
Two sheets of
paper
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 Accuracy
Low Precision
High Precision
Low Accuracy
High Accuracy
High 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
5/8
7/8
The Inch
• Half of an eighth = 1/16 inch
1/16
5/16 9/16 13/16
3/16
7/16 11/16 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?
3/16
1/4 1/2
1/8
Measurement: Using a Fractional Scale
• How long is the rectangle?
What is the
midpoint of 2 1/8
and 2 3/16?
5/32
1/8
3/16
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
Find the average
of the two
measurements
5
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.
2 5 in.
32
• Record decimal equivalent to the nearest
hundredths of an inch.
2.16 in.
Your Turn
Record each measurement in fractional
and decimal inches.