Download - 6.1 using mathematics
![Page 1: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/1.jpg)
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.
![Page 2: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/2.jpg)
Why is mathematics importantMathematics 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
![Page 3: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/3.jpg)
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
![Page 4: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/4.jpg)
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
![Page 5: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/5.jpg)
Health visitor
![Page 6: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/6.jpg)
Pharmacy technician
![Page 7: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/7.jpg)
Forensic scientist
![Page 8: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/8.jpg)
Manufacturing calibration control technician
![Page 9: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/9.jpg)
6.1 Using mathematical tools in science
![Page 10: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/10.jpg)
Key terms
• Standard form• Unit• SI units• Imperial units• Metric units• Prefix• Denominator• Numerator• Ratio• Mensuration
![Page 11: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/11.jpg)
How many?
![Page 12: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/12.jpg)
How many?
![Page 13: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/13.jpg)
How many?
![Page 14: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/14.jpg)
How many?
![Page 15: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/15.jpg)
How many?
![Page 16: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/16.jpg)
What does this mean
• To get a feel of how big numbers are we needs to think in terms of single figures
![Page 17: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/17.jpg)
We also deal with the very big and the very small
![Page 18: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/18.jpg)
![Page 19: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/19.jpg)
![Page 20: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/20.jpg)
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
![Page 21: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/21.jpg)
Standard form
• 6 000 000 000 000 000 000 000 000 kg
• 6.0 x 1024 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
![Page 22: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/22.jpg)
Worked example• Write 300 000 000 m/s in standard form• 300 000 000.0 = 300000000.0 x100
• 300 000 000.0 = 30000000.00 x101
• 300 000 000.0 = 3000000.000 x102
• 300 000 000.0 = 300000.0000 x103
• 300 000 000.0 = 30000.00000 x104
• 300 000 000.0 = 3000.000000 x105
• 300 000 000.0 = 300.0000000 x106
• 300 000 000.0 = 30.00000000 x107
• 300 000 000.0 = 3.000000000 x108
• 3.0 x108 m/s
![Page 23: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/23.jpg)
Write the following in standard form:
• 15000000000000000000000
• 98000000000000000000000000000
• 435000000000000000000000000
• 23000000000
• 1700000000000000000
• 14000000000000
• 290000000000000000000000000
• 110000000
![Page 24: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/24.jpg)
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
![Page 25: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/25.jpg)
Write the following in standard form
• 0.00000000000000345
• 0.00267
• 0.0000000000000000000000000089
• 0.00000000000000000000002
• 0.0000000000000045
• 0.000000000000000000000000077
• 0.000000000000000000000000000001
• 0.00000000000000092
![Page 26: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/26.jpg)
![Page 27: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/27.jpg)
Imperial system
![Page 28: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/28.jpg)
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?
![Page 29: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/29.jpg)
SI (metric) systemPhysical 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
![Page 30: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/30.jpg)
6.2 Collecting and recording scientific data
![Page 31: 6.1 using mathematics](https://reader031.vdocuments.us/reader031/viewer/2022020716/5556f55ed8b42ac60c8b522b/html5/thumbnails/31.jpg)
6.3 Displaying and interpreting scientific data