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 length mass force time thermodynamic temperature Symbol in.

ft mi slug lb s F inch Foot mile slug pound second Unit 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

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 3/16 5/16 7/16 9/16 13/16 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?

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 32 in.

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

2.16 in.

Your Turn

Record each measurement in fractional and decimal inches.