Mathematical Fundamentals

SI System Standard International System of measurement – metrics Has seven base units and many other units derived from these seven

Seven Base Units Quantity Unit Abbreviation length meter m mass gram g time second s temperature kelvin K amount mole mol current ampere amp intensity candela cd

Derived Units Many other units are used in the metric system, but they are combinations of the base units Volume - volume = length x width x height (m) x (m) x (m) = m m 3 = 1 liter (L) - 1 cm 3 = 1ml

Prefixes Metric system utilizes prefixes which indicate multiples of 10 of the unit kilo- k1000 hecto- h 100 deka- da 10 deci- d.1 centi- c.01 milli- m.001

Converting Between Metric Units 3.65 dam = __________cm 2587 mm = __________hm.0087 hl = __________cl

More Prefixes Tera-T10 12 Giga-G10 9 Mega- M 10 6 Micro- u10 -6 Nano - n10 -9 Pico- p10 -12

Use the appropriate prefixes 3 x 10 6 L 15 x g 8 x 10 8 m 3.5 x A 1.46 x J

Temperature Metric unit – Kelvin – not used for measurement Measured in  C (celsius) K =  C Old system is  F (farenheit) C = 5/9 (F -32) What is 69  F in  C and K?

Temperature is an intensive property- does not depend on the amount Extensive properties do depend on the amount In the statement “a yellow sample is solid at 25 C. It weighs 6.0g and has a density of 2.3g/cm 3 ” what are the intensive and extensive properties?

Uncertainty We do not know infinite digits of a measurement Exact numbers are known for sure Inexact – have some question (estimates)

Precision and Accuracy Accuracy refers to the agreement of a particular value with the true value. Precision refers to the degree of agreement among several measurements made in the same manner. Neither accurate nor precise Precise but not accurate Precise AND accurate

Reporting Numbers In recorded measurements, all the digits are considered exact up until the last digit which may be off by one ±.0001 All digits including the uncertain one are called significant figures We are fairly confident of these digits Further uncertainty can be eliminated by repeating the experiment

Which Digits Are Significant? Any non-zero number is significant Any number to the left of a decimal is significant Zeros to the right of a decimal and behind other numbers are significant Zeros to the right of a decimal but in front of other numbers are not significant

How many Significant Figures in each below? 1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )

Round each to 3 Significant Figures 1) ) ) ) ) ) ) ) ) )

Multiplying and Dividing Multiply or divide the number out as normal but round the answer to the least number of significant figures in the problem

Solve each with correct Sig Figs 1) 2.4 x = 2)  = 3) (5.682 x 10 5 ) x (2.87 x 10 4 ) = 4) (2.145 x )  (6.75 x 10 4 ) =

Addition and Subtraction Add or subtract as normal but round the answer with the same number of decimal places as the quantity in the calculation having the least

Solve each with correct Sig Figs 1) 5.44 – ) ) 87.3 – ) 8.2 – 7.11

Conversions Often the units must be changed in order to do a problem Conversion factor method Is utilized A26

Examples How many inches in 3.5 km? A chemical reaction produces 3.5 x atoms of product every hour. How many will be produced in 2.5 hours? How many square cm in a square inch?

Density Identification tag for a substance Every substance has a unique density

The density of silver is 10.5 g/cm 3. If 5.25g of silver pellets are added to a graduated cylinder containing 11.2 ml of water, to what volume will the water rise?