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Using Numbers in Science Metric System and Instruments Used for Measurement

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## Using Numbers in Science Metric System and Instruments Used for Measurement

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**Using Numbers in ScienceMetric System and Instruments Used**for Measurement**Parts of a Measurement**• The value (numerical portion) • The unit (describes what units) • The name of substance being measured EX: 1 teaspoon salt 2 liters of pop**Scientific Measurements**• Made in metric units • Referred to as the International System or SI units • Based on the decimal system • Related by powers of 10 • Each type has a base unit • Use prefixes to refer to a unit larger or smaller than the base by some power of 10**Review of Metric System**• Nano = 1/100,000,000 = 0.000000001 • Micro = 1/1,000,000 = 0.000001 • XXX • XXX • Milli = 1/1,000 = 0.001 • Centi = 1/100 = 0.01 • Deci = 1/10 = 0.1 • BASE UNIT = 1 • Deca = 10 = • Hecto = 100 • Kilo = 1000**Comparison Ideas**equals equals**SI (International System) units**Centigrade or Celsius = ºC This is the unit we will use in lab for temperatures!**Uncertainty in Measurement**• No matter how careful you are • No matter how carefully you read the measuring instrument • No measurement is perfectly accurate • The quality of our measurements are stated in terms of accuracy and precision**Uncertainty in Measurement**Measured numbers -are an estimated amount -measured to a certain number of significant figures -a numerical value with attached units that expresses a physical quantity such as length, mass, volume, time or temperature.**Uncertainty in Measurements**• Error: is the difference between the true value and our estimate, or measurement, of the value. • Accuracy: is the degree of agreement between the true value and the measured value. • Precision: is a measure of the agreement of replicate measurements • Uncertainty: is the degree of doubt in a single measurement.**Accuracy**= of a measurement is how close that measurement is to the true or “exact” value EX: Standard weight = 5.00g 4.98g more accurate than 5.12 g**Accuracy**• Also subject to the reliability of the measuring instrument • The smaller the increments of units on the instrument, the more accurate**Length Measurements**Measuring the length of a metal rod • Ruler A has more uncertainty and gives less precise measurements. • Ruler B has less uncertainty and gives more precise measurements. Metric Rulers for Measuring Length.**Precision**• Precision = making reproducible or repetitive measurements of the same quantity • How fine the divisions are • There will always be some uncertainty because of the limits in the accuracy of your instruments**Precision versus Accuracy**Precise but inaccurate Precise and accurate It is also possible to have an accurate measurement without being precise. Imprecise and inaccurate**“Accuracy is telling the truth…..**Precision is telling the same story over and over again.” Yiding Wang yiang@mtu.edu**Strive for measurements that are accurate and precise**Measurements you perform will be used in subsequent calculations In scientific measurements all the digits known w/certainty, plus the one estimated digit, are known as significant figures or significant digits.**Significant Figures**Significant figures: is defined to be all digits in a number representing data or results that are known with certainty plus the first uncertain digit. 5.4 cm 7 0 1 2 3 5 8 4 6 9 10 cm 5.48 cm 7 0 1 2 3 5 8 4 6 9 10 cm**Significant figures or Significant digits**• ANY numbers generated by means of a measurement (length, volume, time, etc) should be expressed in the correct number of significant figures. • This reflects how close the measured values are to the true values.**Significant Figures (digits)**= reliable figures obtained by measurement = all digits known with certainty plus one estimated digit**Taking the measurement**• Is always some uncertainty • Because of the limits of the instrument you are using**EXAMPLE: mm ruler**Is the length of the line between 4 and 5 cm? Yes, definitely.Is the length between 4.0 and 4.5 cm? Yes, it looks that way. But is the length 4.3 cm? Is it 4.4 cm?**It is important to be honest when reporting a measurement,**so that it does not appear to be more accurate than the equipment used to make the measurement allows. • We can achieve this by controlling the number of digits, or significant figures, used to report the measurement.**As we improve the sensitivity of the equipment used to make**a measurement, the number of significant figures increases.**5,551,213**55.00 mm Which numbers are Significant? How to count them! 9000 L 0.003g**Non-Zero integers**• Always count as significant figures 1235 has 4 significant digits**Zeros – there are 3 types**Leading zeros (place holders) The first significant figure in a measurement is the first digit other than zero counting from left to right 0.0045g (4 is the 1st sig. fig.) “0.00” are place holders. The zeros are not significant**Captive zeros**Zeros within a number at always significant – 30.0809 g All digits are significant**Trailing zeros – at the end of numbers but to the right of**the decimal point 2.00 g - has 3 sig. digits (what this means is that the measuring instrument can measure exactly to two decimal places. 100 m has 1 sig. digit Zeros are significant if a number contains decimals**Exact Numbers**Are numbers that are not obtained by measuring Referred to as counting numbers EX : 12 apples, 100 people**Exact Numbers**Also arise by definition 1” = 2.54 cm or 12 in. = 1 foot Are referred to as conversion factors that allow for the expression of a value using two different units**Significant Figures**• Rules for sig figs.: • Count the number of digits in a measurement from left to right: • Start with the first nonzero digit • Do not count place-holder zeros. • The rules for significant digits apply only to measurements and not to exact numbers Sig figs is short for significant figures.**Determining Significant Figures**State the number of significant figures in the following measurements: 2005 cm 4 0.050 cm 2 2 3 25,000 g 0.0280 g 3 4 25.0 ml 50.00 ml 0.25 s 2 1000 s 1 0.00250 mol 3 1000. mol 4**Rounding Numbers**• To express answer in correctly • Only use the first number to the right of the last significant digit**Rounding**• Always carry the extra digits through to the final result • Then round EX: Answer is 1.331 rounds to 1.3 OR 1.356 rounds to 1.4**Significant Figures**Rounding off sig figs (significant figures): Rule 1: If the first non-sig fig is less than 5, drop all non-sig fig. Rule 2: If the first sig fig is 5, or greater that 5, increase the last sig fig by 1 and drop all non-sig figs. Round off each of the following to 3 significant figures: 12.514748 12.5 0.6015261 0.602 14652.832 14,700 192.49032 192**Measurements With a Ruler orMeter Stick – Look at it**FIRST! – Where is “0”**Using a Vernier**Caliperhttp://phoenix.phys.clemson.edu/labs/cupol/vernier/ • Used to accurately determine the fraction part of the least count division. • Length of an object, the outer diameter (OD) of a round or cylindrical object, the inner diameter (ID) of a pipe, and the depth of a hole.**Main scale**Auxillary (Venier) Scale • The caliper consists of a main scale engraved on a fixed ruler and an auxiliary caliper scale engraved on a movable jaw • The movable auxiliary scale is free to slide along the length of the fixed ruler. • The main scale is calibrated in centimeters with the smallest division in millimeters. • The auxiliary scale has 10 divisions that cover the same distance as 9 divisions on the main scale. Therefore, the length of the auxiliary scale is 9.0 mm.**When the caliper is closed and properly zeroed the first**mark (zero) on the main scale is aligned with the first mark on the auxiliary scale. • The last mark on the auxiliary scale will then coincide with the 9 mm-mark on the main scale. • This is read 0.00 cm.**Once the caliper is positioned to make a reading, make a**note of where the first mark on the auxiliary scale falls on the main scale. • We see that the object's length is between 1.2 cm and 1.3 cm because the first auxiliary mark is between these two values on the main scale.