# SI Measurement System US Customary Measurement System &

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<ul><li><p>SI Measurement SystemUS Customary Measurement System&</p></li><li><p>The International System of Units (SI)The International System of Units (SI) is a system of units of measurement consisting of seven base units</p><p>Mostly widely used system of measurementUnited States is the only industrialized nation that has not adopted the SI system</p><p>Unit NameSymbolMeasurementmetermlengthkilogram*kgmasssecondstimeampereAelectric currentkelvinKthermodynamic temperaturecandelacdluminous intensitymolemolamount of substance</p></li><li><p>The International System of UnitsOften referred to as the metric scalePrefixes indicate an integral power of 10</p><p>Power of 10PrefixAbbreviation101deca-da102hecto-h103kilo-k106Mega-M109Giga-G1012Tera-T</p><p>Power of 10PrefixAbbreviation10-1deci-d10-2centi-c10-3milli-m10-6micro-10-9nano-n10-12pico-p</p></li><li><p>Common Items: Size ComparisonU S Customary SystemS I</p></li><li><p>Recording MeasurementsMeasurements must always include unitsMeasurements are the best estimate of a quantityThey are not an exact amountA measurement is only good if you know that it is reasonable close to the actual quantityIt is important to indicate the accuracy and precision of your measurementsScientists and engineers use significant digits to make the accuracy and precision of measurements clear</p></li><li><p>Precision and AccuracyPrecision = the degree to which repeated measurements show the same resultAccuracy = the degree of closeness of measurements of a quantity to the actual (or accepted) valueHigh AccuracyLow PrecisionHigh PrecisionLow AccuracyHigh AccuracyHigh Precision</p></li><li><p>Recording MeasurementsIdeally, a measurement device is both accurate and preciseAccuracy depends on calibration to a standardPrecision depends on the characteristics and/or capabilities of the measuring device and its useUse significant digits to indicate the accuracy and precision of experimental resultsRecord only to the precision to which you and your measuring device can measure</p></li><li><p>Significant DigitsAccepted practice in science is to indicate accuracy and/or precision of measurementSignificant digits are digits in a decimal number that carry meaning contributing to the precision or accuracy of the quantityThe digits you record for a measurement are considered significantInclude all certain digits in a measurement and one uncertain digitNote: fractions are fuzzy numbers in which significant digits are not directly indicated</p></li><li><p>Recording MeasurementsManufacturers of equipment usually indicate the accuracy and precision of the instrumentGeneral RulesDigital Instruments read and record all the numbers, including zeros after the decimal point, exactly as displayedDecimal Scaled Instruments record all digits that you can certainly determine from the scale markings and estimate one more digitPreferred over fractional scaled instrumentsFractional Scaled Instruments need special consideration</p></li><li><p>Metric ScaleA typical metric scale often includes a 30+ centimeter graduated scaleEach centimeter is graduated into 10 millimeters</p></li><li><p>The MillimeterThe millimeter is the smallest increment found on a typical SI scale1 mm</p></li><li><p>The MillimeterThe next larger marking on a SI scale shows 5 millimeters5 mm</p></li><li><p>The MillimeterLargest markings on a SI scale represents centimeters (cm)These are the only marks that are actually numbered. 1 cm = 10 mm</p></li><li><p>Measurement: Using a Decimal ScaleHow long is the rectangle?Lets look a little closer</p></li><li><p>Measurement: Using a Decimal ScaleHow long is the rectangle?</p></li><li><p>Recording a MeasurementHow long is the rectangle?Remember the General RuleDecimal Scaled Instruments record all digits that you can certainly determine from the scale markings and estimate one more digitBest Estimate = 3.84 cm</p></li><li><p>Recording a MeasurementHow long is the rectangle?Remember the General RuleDecimal Scaled Instruments record all digits that you can certainly determine from the scale markings and estimate one more digitBest Estimate = 3.84 cm</p></li><li><p>Your TurnHow would you record the length of this rectangle?</p><p>How many significant digits?6.33 cm3</p></li><li><p>Fractional Length MeasurementA typical ruler providesA 12 inch graduated scale in US Customary unitsEach inch is graduated into smaller divisions, typically 1/16 increments</p></li><li><p>The InchThe divisions on an U S Customary units scale are easily identified by different sized markings. The largest markings on the scale identify the inch. </p></li><li><p>The InchEach subsequently shorter tick mark indicates half of the distance between next longer tick marksFor example the next smaller tick mark indicates half of an inch = inch1/2</p></li><li><p>The InchHalf of a half = inch. An English scale shows inch and inch marks.All fractions must be reduced to lowest terms1/43/4</p></li><li><p>The InchHalf of a quarter = 1/8 inch1/83/87/85/8</p></li><li><p>The InchHalf of an eighth = 1/16 inch1/163/165/1613/167/1611/169/1615/16</p></li><li><p>Measurement: Using a Fractional ScaleHow long is the rectangle?Lets look a little closer</p></li><li><p>Measurement: Using a Fractional ScaleHow long is the rectangle?What fraction of an inch does this mark represent?1/21/41/83/16</p></li><li><p>Measurement: Using a Fractional ScaleHow long is the rectangle?What is the midpoint of 2 1/8 and 2 3/16?5/32</p></li><li><p>Measurement: Using a Fractional ScaleHow do we determine that 5/32 is midway between 1/8 and 3/16?Convert each fraction to a common denominator: 325Find the average of the two measurements</p></li><li><p>Recording a Measurement: Using a Fractional ScaleHow long is the rectangle?Remember the General RuleFractional Scaled Instruments require special considerationIs 6 significant digits appropriate???1/16 in. = .0625 in.</p></li><li><p>Recording a Measurement: Using a Fractional ScaleFor the standard ruler marked in 1/16 inch incrementsRecord fraction measurements to the nearest 1/32 inch.</p><p>Record decimal equivalent to the nearest hundredths of an inch.</p></li><li><p>Instant Challenge</p><p>http://www.globalclassroom.org/rulergame200/index.htmlLog on to the following websiteYou will have 90 seconds to compete against a classmateWinners will continue on to the next round to see who is the RULER of the Class</p><p>Note that even though kilogram has the kilo- prefix, it is defined as a base unit and is used in definitions of derived units. Presentation NameCourse NameUnit # Lesson #.# Lesson Name*Note that the kilo- prefix in kilogram indicates that a kilogram is 10^3 = 1000 grams. The fact that the kilogram is a base unit does not affect the meaning of the prefix but allows for the use of the kilogram as a unit in the definition of derived units.</p><p>[These, and additional prefixes are shown on the PLTW Engineering Formula Sheet. Students do not need to write these prefixes in their notes.]</p><p>Presentation NameCourse NameUnit # Lesson #.# Lesson Name*Students can understand more when you relate to common objects.</p><p>Presentation NameCourse NameUnit # Lesson #.# Lesson Name*Be sure to always include units when recording measurements.</p><p>There are always errors in measurements, even if they are very small. It is important to know the level of error that may be inherent in a measurement. </p><p>It is important to understand how accurate the recorded measurement is. For instance, if you know an object measures 3 inches in length, you cant really be sure if the object is actually somewhat longer or shorter than 3 inches. Perhaps the object is 3 1/16 inches long, or 2 15/16 inches long. If the object must fit into a 3 inch space which again may be somewhat larger or smaller than the recorded measurement. How can you be sure the part will fit?Presentation NameCourse NameUnit # Lesson #.# Lesson Name*Although precision and accuracy are often confused, there is a difference between the meanings of the two terms in the fields of science and engineering.Precision indicates how close together repeated measurements of the same quantity are to each other. So, a precise bathroom scale would give the same weight each time you stepped on the scale within a short time (even if it did not report your true weight).Accuracy indicate how close measurements are to the actual quantity being measured. For example, if you put a 5 pound weight on a scale, we would consider the scale accurate if it reported a weight of 5 pounds. </p><p>A target analogy is sometimes used to differentiate between the two terms. Consider the arrows or dots on the targets to be repeated measurements of a quantity. [click] The first target shows that the arrows (or repeated measurements) are centered around the center of the target, so on the whole, the measurements are fairly close to the target (actual) measurement making the measuring devise accurate. But the repeated measurements are not close to each other - so the precision of the measuring device is low. , although they are not close to each other. [click] The second target show that the arrows (or repeated measurements) are close together so the precision is high. But the center of the measurements is not close to the target (actual) value of the quantity.What should the target look like if the measurement is both highly accurate and highly precise? [allow student to answer then click]. The third target shows both precision (because the measurement are close together) and accuracy (because the center or the measurements is close to the target value).Presentation NameCourse NameUnit # Lesson #.# Lesson Name*Laying tile involves accuracy, so significant figures are useful. Let's say you want to know how wide 10 tiles would go. You measure one tile and you get 11 7/8 inches on one side of the tape measure and 30.2 centimeters on the other side. If you convert 11 7/8 inches to decimal fraction, you get 11.875 inches. That implies accuracy down to a thousands of an inch. That isn't true because the tape can't measure to the nearest thousandths of an inch. Only to the nearest 16th of an inch. So significant numbers are easier to determine when a measurement is done with decimal fractions.Presentation NameCourse NameUnit # Lesson #.# Lesson Name*We will concentrate on measuring and recording linear length measurements in this presentation, but the techniques discussed apply to all types of measurements.</p><p>Well look at an example of a decimal scaled instrument first a metric scale. Later well talk about a fractional scale a ruler divided into fractions of inches. </p><p>Presentation NameCourse NameUnit # Lesson #.# Lesson Name*Lets look a little closer. [click]Presentation NameCourse NameUnit # Lesson #.# Lesson Name*You can tell that the length of the rectangle is between 3 and 4 centimeters. [click]</p><p>And, because the scale is incremented in millimeters, you can also be certain that the measurement is between 3.8 and 3.9 centimeters (assuming the scale is accurate). So, you are certain that the first digit after the decimal, the tenths place, is 8. [click]</p><p>But, because there are no tick marks between millimeter marks, you can only estimate the hundredths place of the measurement. Perhaps you would estimate 3.83 or 3.84 cm. The last digit is an estimate your best guess as to where, within the millimeter distance, the measurement falls.</p><p>Presentation NameCourse NameUnit # Lesson #.# Lesson Name*Since the measurement is certainly between 3.8 and 3.9, you can be certain that the 3 and the 8 are correct. However, the 4 is an estimate based on your best guess.</p><p>This number has three significant digits : 3, 8 and 4.</p><p>Presentation NameCourse NameUnit # Lesson #.# Lesson Name*[click to zoom in on scale. Allow student to estimate the measurement.][click to reveal estimate of 6.33 cm.]</p><p>Answers may vary, but a good estimate that reflects the appropriate precision is 6.33 cm. Other good estimates are 6.32 or 6.34 cm. </p><p>[Click and allow students to answer question then click again to reveal answer of 3.]Presentation NameCourse NameUnit # Lesson #.# Lesson Name*In this presentation, we will concentrate on linear measurements of length.Presentation NameCourse NameUnit # Lesson #.# Lesson Name*[click to zoom in on scale. Allow student to estimate the distance then click again.]Presentation NameCourse NameUnit # Lesson #.# Lesson Name*You can tell that the length of the rectangle is between 2 and 3 inches. So the first inch digit of the number is certainly 2. </p><p>[slowly click through , , and 1/8 indicators. Then click to reveal question. Allow students to answer then click again.</p><p>[click] And, because the scale is incremented in 16ths of an inch, you can also be certain that the measurement is between 2 1/8 in. and 2 3/16 in. (assuming the scale is accurate). Presentation NameCourse NameUnit # Lesson #.# Lesson Name*[click] We may be tempted to estimate the length to be right in the middle. What is the midpoint between these two tickmarks? [Allow students to answer then click]. 2 5/32.Presentation NameCourse NameUnit # Lesson #.# Lesson Name*To determine the midpoint on the scale, convert both endpoint fractions to 32nds of an inch. This is done my multiplying the fraction by another fraction that is equal to one. In other words, multiply by a fraction with the same factor in the numerator and the denominator. In order to convert a fraction in eighths to a fraction in terms of 32nds, multiply by 4 / 4. [click]</p><p>To convert a fraction in terms of eights of an inch to 32nds of an inch, multiply by 2/2. [click]</p><p>The midpoint is represented by the average of these two numbers. [click]Presentation NameCourse NameUnit # Lesson #.# Lesson Name*Since the measurement is certainly between 2 and 3 inches, you can be certain that the 2 is correct. </p><p>You are also certain the measurement is between 2 1/8 = 2 2/16 and 2 3/16. What does that mean with respect to significant figures? Significant digits dont really apply to fractions, so lets convert the fraction to a decimal.</p><p>The decimal equivalent of 2 5/32 is 2.15625 inches. If we assume all of these figures are significant, it would suggest that we are certain of the measurement to the nearest ten thousandth of an inch and that we estimated the one hundred thousandth of an inch. There is NO WAY we can be that accurate with a standard ruler that shows 1/16 inch increments. </p><p>Since we can be certain of the measurement to the nearest 1/16 inch which is equivalent to approximately 0.06 inches, estimates to the nearest 0.01 in would be an estimate.Presentation NameCourse NameUnit # Lesson #.# Lesson Name*So, for our purposes here, we will record measurements made on a fractional scale (incremented to the 1/16 inch) to the nearest 1/32 inch.</p><p>But when converting the number to a decimal we will record the number to the hundredths place such that the tenths place is certain and the hundredths place is estimated.Presentation NameCourse NameUnit # Lesson #.# Lesson Name*</p></li></ul>

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