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) = m3

- .001 m3 = 1 liter (L)

- 1 cm3 = 1ml

Prefixes

Metric system utilizes prefixes which indicate multiples of 10 of the unit

kilo- k 1000 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- T 1012

Giga- G 109

Mega- M 106

Micro- u 10-6

Nano - n 10-9

Pico- p 10-12

Use the appropriate prefixes

3 x 106 L

15 x 10-9 g

8 x 108 m

3.5 x 10-6 A

1.46 x 1010 J

Temperature

Metric unit – Kelvin – not used for measurement

Measured in C (celsius) K = C + 273.15

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/cm3” 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 AccuracyAccuracy 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

2.2405 ± .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) 28.6 9) 3440.

2) 910 10) 0.04604

3) 0.0076000 11) 804.05

4) 0.0144030 12) 1002

5) 400 13) 400.

6) 700.0 14) 0.000625000

7) 0.4004 15) 6000

8) 1.30 16) 0.00067

Round each to 3 Significant Figures

1) 31.068 6) 149.51

2) 2.613 7) 6.561

3) 81.436 8) 13.1252

4) 0.001567 9) 143.81

5) 1.1353 10) 0.000355

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 15.82 =

2) 94.20 3.16722 =

3) (5.682 x 105) x (2.87 x 104) =

4) (2.145 x 10-5) (6.75 x 104) =

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 – 2.6103

2) 2.099 + 0.05681

3) 87.3 – 1.655

4) 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 1025 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

MassDensity

Volume

The density of silver is 10.5 g/cm3. 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?