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Using mathematical tools for science

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1 Using mathematical tools for science
To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.

2 Why is mathematics important
Mathematics touches all of our lives. Whether you work as a health visitor monitoring the mass of newborn babies or as a NASA technician assisting with the design of new engines, you will work with numbers and very likely you will want to display data. Being able to leave your calculations to the appropriate significant figures and in standard form will be vital. This unit will provide you with plenty of examples to master this skill

3 Learning outcomes Be able to use mathematical tools in science
Be able to collect and record scientific data Be able to display and interpret scientific data

4 Maths for science In small groups, discuss what kind of maths may be used by the following professionals: Health visitor Pharmacy technician Forensic scientist Manufacturing calibration control technician For example, do they use fractions, algebra, charts or graphs? What do they use the maths to do in their work? What maths tools are common to all and which tools might only apply to each profession? Present your results as a poster

5 Health visitor

6 Pharmacy technician

7 Forensic scientist

8 Manufacturing calibration control technician

9 6.1 Using mathematical tools in science

10 Key terms Standard form Unit SI units Imperial units Metric units
Prefix Denominator Numerator Ratio Mensuration

11 2 How many?

12 5 How many?

13 14 How many?

14 49 How many?

15 85 How many?

16 What does this mean To get a feel of how big numbers are we needs to think in terms of single figures 1-10

17 We also deal with the very big and the very small

18 The very small…

19 The very big…

20 Differences in size The diameter of an influenza virus is about 0.8 nanometers or numerically m The average Earth-Sun distance is 150 million kilometers or numerically m

21 Standard form kg 6.0 x 1024 kg Number between 1 and 10 24 Is the power of 10, which means 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x10 x 10 x 10: 10 x itself 23 more times The power of 10 is increased by moving the decimal point left for big numbers of right for small numbers

22 Worked example Write 300 000 000 m/s in standard form
3.0 x108 m/s

23 Write the following in standard form:

24 Very small numbers We do something similar with small numbers like the mass of a proton which is kg kg = 1.67 x kg

25 Write the following in standard form

26

27 Imperial system

28 The problem 12 inches in a foot 3 feet in a yard
220 yards in a furlong 1760 yards in a mile How can you remember all these?

29 SI (metric) system Physical quantity Name of units Symbol for unit
Length Metre M Time Second S Mass Kilogram Kg Temperature Kelvin K Amount of substance Mole Mol Electric current Ampere A Luminous intensity candela cd

30 6.2 Collecting and recording scientific data

31 6.3 Displaying and interpreting scientific data


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