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Mathematics for engineering technicians Unit 4

Mathematics for engineering technicians Unit 4. Handout No. 1 I Ford. Numbers. Engineers use a lot of numbers as they are precise. For example, instead of saying a ‘large storage tank’ we would be more specific such as ‘a tank with a capacity of 4,500 litres’.

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Mathematics for engineering technicians Unit 4

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  1. Mathematics for engineering techniciansUnit 4 Handout No. 1 I Ford

  2. Numbers • Engineers use a lot of numbers as they are precise. • For example, instead of saying a ‘large storage tank’ we would be more specific such as ‘a tank with a capacity of 4,500 litres’. • When engineers draw up a specification they do so using numbers and drawings in preference to written descriptions.

  3. Units and symbols • Engineering as in science uses a large number of units and symbols. • It is important that you get to know the common units and get to recognise their abbreviations and symbols. • The units used are part of the International System (known as SI) of units.

  4. Fundamental SI units

  5. Multiples and sub-multiples • Unfortunately, the numbers that we deal with in engineering can sometimes be very large or very small. Example 1: the voltage of a VHF radio could be as little as 0.0000015 V. Example 2: the resistance present in an amplifier stage could be as high as 10,000,000 Ώ • Having to take into account all the zero’s can be a bit of a problem. We can make life a lot easier by using a standard range of multiples and sub-multiples. • These use a prefix letter that adds a multiplier to the quoted value.

  6. Some common prefixes & multipliers

  7. Examples • An amplifier requires an input voltage of 50 mV. Express this in V. • An aircraft strut has a length of 1.25m. Express this in mm. • A marine radar operates at a frequency of 9.74 GHz. Express this in MHz. • A generator produces a voltage of 440 V. Express this in kV. • A manufacturing process uses a coating with a thickness of 0.075 mm. Express this in μm. • A radar transmitter has a frequency of 15.62 MHz. Express this in kHz. • A current of 570 μA flows in a transistor. Express this current in mA. • A capacitor has a value of 0.22μF. Express this in nF. • A resistor has a value of 470 kΏ. Express this in MΏ. • A plastic film has a thickness of 0.0254 cm. Express this in mm. (Answers: 1=0.05V 2=1250mm 3=9740mm 4=0.44kV 5=75m 6=15,620kHz 7=0.57mA 8=220nF 9=0.47M Ώ 10=0.254mm)

  8. INTEGERS Positive (+) 1, 2, 3, 4, ….., Negative (-) -1, -2, -3, -4, ….., You do not need to show the + sign as we assume that it is there! Fig.1 The number line (showing positive & negative integers) • The number of units that a number is from zero (regardless of direction or sign) is known as the absolute value) • Positive values are to the right whilst negative are to the left • The number zero (0) is neither a positive or negative integer.

  9. Numbers between two integer numbers • Engineers frequently have to deal with numbers that lie between two integer numbers • Therefore, integers are not precise enough for engineering applications • We can get over this problem in two ways: • Use fractions • Use a decimal point • For example, the number that sits half way between 3 and 4 can be expressed as 3½ or 3.5

  10. Laws of signs(Directed numbers) There are four basic laws for using signs:

  11. 8 + 7 (15) -13 – 12 (-25) -8 – 9 (-17) 5 + 8 (13) 7 – 11 (-4) 8 – 16 (-8) -5 – 12 (-17) -4 + 8 (4) 11 – 5 (6) -8 – 10 (-18) -7 -5 -4 (-16) -6 + 8 -3 (-1) 17 – 8 – 5 (4) 20 – 19 – 8 + 3 (-4) 8 – (+5) (3) -4 – (-7) (3) 8 – (-3) (11) -6 – (-2) (-4) -5 – (+6) (-11) -3 – (-6) – (-4) (7) 5 x 4 (20) (-5) x 4 (-20) 5 x (-4) (-20) (-5) x (-4) (20) (-3)² (9) (-8)² (64) 3 x (-4) + 2 x (-3) (-18) (-3) x (2) – (-2) x 4 (2) 6 / 3 (2) 6 / (-3) (-2) (-6) / (3) (-2) (-6) / (-3) (2) (-10) / (-5) (2) 1 / (-1) (-1) (-1) / 1 (-1) (-3) x (-4) / (-2) (-6) Examples on directed numbers

  12. Formulae • Formulae play a very important part in engineering as by using them, it is possible to give a clear and accurate statement of physical laws • E.G. OHMS LAW : V = I x R • The value that we are attempting to find is known as the SUBJECT.

  13. BODMAS • This gives the order (sequence) in which operations should be done when solving an equation. Example : 4 + 3 x 2 = ?? • Which operation do we do first, Add or multiply? • We get a different answer depending on what we do first. • In order to get the right answer, we multiply first: 4 + 6 = 10

  14. BODMAS RULE B : BRACKETS O : ORDER (Powers and square roots) D : DIVISION M : MULTIPLICATION A : ADDITION S : SUBTRACTION

  15. BODMAS EXAMPLE 30 – (2 x 32 + 5) BRACKETS 1st then use ODMAS inside the brackets 30 - (2 x 9 + 5) (ORDER 32) 30 – (18 + 5) (MULTIPLY 2 x 9) 30 – 23 (ADD 18 + 5) Answer = 7

  16. Examples • 42 + (6 x 3 – 32) 25 • 24 – (72 + 42 – 82) 23 • 12 x (22 x 5 – 15) 60 • 6 ( 9 – 3) 36 • 4 (32 x 5 – 15) 120 • 32 (15 – 4 x 3) 27 • 7 – 4 (60 – 2 x 7 + 3 - 29) 60 • (6 x 3 – 32) + (22 x 5 – 15) 14

  17. Significant figures • When doing calculation using formulas, the answers are sometimes very long. • Complete the following table:

  18. Decimal Places • Sometimes we are more interested in the number of digits (to the right) after the decimal point. • Complete the following table:

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