The International System of Units (SI) The International System of Units (SI) is a system of units of measurement consisting of seven base units Mostly widely used system of measurement United States is the only industrialized nation that has not adopted the SI system Unit NameSymbolMeasurement metermlength kilogram*kgmass secondstime ampereAelectric current kelvinKthermodynamic temperature candelacdluminous intensity molemolamount of substance

The International System of Units Often referred to as the metric scale Prefixes indicate an integral power of 10 Power of 10PrefixAbbreviation 10 1 deca-da 10 2 hecto-h 10 3 kilo-k 10 6 Mega-M 10 9 Giga-G Tera-T Power of 10PrefixAbbreviation deci-d centi-c milli-m micro-µ nano-n pico-p

Common Items: Size Comparison Two sheets of paper Human hair Diameter of paper clip 0.2 mm.0.1 mm0.8 mm U S Customary System S I

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 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

2.4 Measurement and Significant Figures Every experimental measurement has a degree of uncertainty. The volume, V, at right is certain in the 10’s place, 10mL<V<20mL The 1’s digit is also certain, 17mL<V<18mL A best guess is needed for the tenths place.

To indicate the precision of a measurement, the value recorded should use all the digits known with certainty, plus one additional estimated digit that usually considered uncertain by plus or minus 1. No further, insignificant, digits should be recorded. The total number of digits used to express such a measurement is called the number of significant figures. All but one of the significant figures are known with certainty. The last significant figure is only the best possible estimate.

Below are two measurements of the mass of the same object. The same quantity is being described at two different levels of precision or certainty.

When reading a measured value, all nonzero digits should be counted as significant. There is a set of rules for determining if a zero in a measurement is significant or not. RULE 1. Zeros in the middle of a number are like any other digit; they are always significant. Thus, g has five significant figures. RULE 2. Zeros at the beginning of a number are not significant; they act only to locate the decimal point. Thus, cm has three significant figures, and mL has four.

RULE 3. Zeros at the end of a number and after the decimal point are significant. It is assumed that these zeros would not be shown unless they were significant m has six significant figures. If the value were known to only four significant figures, we would write m. RULE 4. Zeros at the end of a number and before an implied decimal point may or may not be significant. We cannot tell whether they are part of the measurement or whether they act only to locate the unwritten but implied decimal point.

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

Metric Scale A typical metric scale often includes a 30+ centimeter graduated scale Each centimeter is graduated into 10 millimeters

The Millimeter The millimeter is the smallest increment found on a typical SI scale 1 mm

The Millimeter The next larger marking on a SI scale shows 5 millimeters 5 mm

The Millimeter Largest markings on a SI scale represents centimeters (cm) These are the only marks that are actually numbered. 1 cm = 10 mm

Measurement: Using a Decimal Scale How long is the rectangle? Let’s look a little closer

Measurement: Using a Decimal Scale How long is the rectangle?

Recording a Measurement How long is the rectangle? Remember the General Rule –Decimal Scaled Instruments – record all digits that you can certainly determine from the scale markings and estimate one more digit Best Estimate = 3.84 cm

Recording a Measurement How long is the rectangle? Remember the General Rule –Decimal Scaled Instruments – record all digits that you can certainly determine from the scale markings and estimate one more digit Best Estimate = 3.84 cm Certain

Your Turn How would you record the length of this rectangle? How many significant digits? 6.33 cm 3

Your Turn Record each measurement in centimeters using the appropriate number of significant digits.