6.1 using mathematics
- 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
- 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. How many?
- 12. How many?
- 13. How many?
- 14. How many?
- 15. 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
- 17. We also deal with the very big and the very small
- 20. Differences in size The diameter of an influenza virus is about 0.8 nanometers or numerically 0.00000008 m The average Earth-Sun distance is 150 million kilometers or numerically 150000000000 m
- 21. Standard form 6 000 000 000 000 000 000 000 000 kg 6.0 x 10 24 kg Number between 1 and 10 The power of 10 is increased by moving the decimal point left for big numbers of right for small numbers 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
- 22. Worked example Write 300 000 000 m/s in standard form 300 000 000.0 = 300000000.0 x10 0 300 000 000.0 = 30000000.00 x10 1 300 000 000.0 = 3000000.000 x10 2 300 000 000.0 = 300000.0000 x10 3 300 000 000.0 = 30000.00000 x10 4 300 000 000.0 = 3000.000000 x10 5 300 000 000.0 = 300.0000000 x10 6 300 000 000.0 = 30.00000000 x10 7 300 000 000.0 = 3.000000000 x10 8 3.0 x10 8 m/s
- 23. Write the following in standard form: 15000000000000000000000 98000000000000000000000000000 435000000000000000000000000 23000000000 1700000000000000000 14000000000000 290000000000000000000000000 110000000
- 24. Very small numbers We do something similar with small numbers like the mass of a proton which is 0.000 000 000 000 000 000 000 000 00167 kg 0.000 000 000 000 000 000 000 000 00167 kg = 1.67 x 10 -27 kg
- 25. Write the following in standard form 0.00000000000000345 0.00267 0.0000000000000000000000000089 0.00000000000000000000002 0.0000000000000045 0.000000000000000000000000077 0.000000000000000000000000000001 0.00000000000000092
- 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