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.

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

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

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

Health visitor

Pharmacy technician

Forensic scientist

Manufacturing calibration control technician

6.1 Using mathematical tools in science

Key terms

• Standard form• Unit• SI units• Imperial units• Metric units• Prefix• Denominator• Numerator• Ratio• Mensuration

How many?

How many?

How many?

How many?

How many?

What does this mean

• To get a feel of how big numbers are we needs to think in terms of single figures

We also deal with the very big and the very small

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

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

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

Write the following in standard form:

• 15000000000000000000000

• 98000000000000000000000000000

• 435000000000000000000000000

• 23000000000

• 1700000000000000000

• 14000000000000

• 290000000000000000000000000

• 110000000

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

Write the following in standard form

• 0.00000000000000345

• 0.00267

• 0.0000000000000000000000000089

• 0.00000000000000000000002

• 0.0000000000000045

• 0.000000000000000000000000077

• 0.000000000000000000000000000001

• 0.00000000000000092

Imperial system

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?

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

6.2 Collecting and recording scientific data

6.3 Displaying and interpreting scientific data