The basic arithmetic operations for real numbers are addition, subtraction, multiplication, and division.
The basic arithmetic properties are the commutative, associative, and distributive properties.
Operations on Numbers
7 + 2 = 9seven and two are nine
seven plus two makes nine
7- 2 = 5seven minus two is five
two from seven leaves five
12 * 4 = 48twelve times four is forty-eight
twelve fours are forty-eight
40 : 1 = 40forty divided by one is forty
one into forty is forty
(9 au carré, 9 puissance 2)
Nine to the power of two
nine to the power of three
Mathematical operations: Examples
5^4five to the fourth
five to the power of four
et ainsi de suite, en utilisant l'adjectif
ordinal, ou la manière plus simple:
nine to the fortieth
nine to the power of forty
la racine carrée de 16 the square root of 16
la racine carrée de 16 est 4 the square root of sixteen is 4
24 > 12 twenty-four is greater than twelve
12 < 25 twelve is less than twenty-five
Mathematical operations: Examples
In algebra, a decimal number can be defined as a number whose whole number part and the fractional part is separated by a decimal point. The dot in a decimal number is called a decimal point. The digits following the decimal point show a value smaller than one.
Decimal Numbers: Examples
0.25naught (zero) point two five
point two five
0.03naught point naught three
0.75naught point seven five
point seven five
3.3 three point three
8.125 eight point one two five
7.2568 seven point two five six eight
EXERCISE : Write in correct English
4.055 = ………………………………………………………………
18 * 100 = 1800………………………………………………………
70 - 8 = 62……………………………………………………………
10: 2= 5………………………………………………………………
Units of MeasureIntroduction
Magnitudes of measurements are typically given in terms of a specific unit. In surveying, the most commonly used units define quantities of length (or distance), area, volume, and horizontal or vertical angles.
The two systems used for specifying units of measure are the Englishand metric systems. Units in the English system are historical units of measurement used in medieval England which evolved from the Anglo-
Saxon and Roman systems. The metric system is a decimalized system of measurement developed in France in late 18th century. Since the
metric system is almost universally used, it is often referred to as the International System of Units and abbreviated SI.
Base Units of Measurements
LengthThe basic unit of length in the SI system is the meter. Subdivisions of the meter are the millimeter, centimeter, and the decimeter, while multiples of meters include the decameter, hectometer, and kilometer.
AreaAreas in the metric system are given is square meters while larger measurements are given in hectares.
VolumeVolumes in the metric system are given in cubic meters.
MassMass refers to the amount of matter in an object. The kilogram is the unit of mass in the metric system.
Angular Measurement In geometry, any horizontal or vertical angle is measured in degrees. These angles maybe given in decimal degrees or degrees, minutes, and seconds. The radian is another unit of measure for angles. By definition, a full circle has 2π radians or 360 degrees.
TemperatureThe Celsius scale, or degrees Celsius (°C), is used in the metric system to measuretemperature.
Example: On the Celsius scale, the freezing point of water is 0°C.
Pressure Atmospheric pressure is the force per unit area exerted against a surface by the weight of the Earth’s atmosphere above that surface. Air pressure is measured in millimeters mercury (mmHg) or millibars (mbars) in the metric system, but may also be measured in Pascals or kilopascals.
Scientific Experiments Description
The scientific method is the process through which hypothesis are developed, tested and also proven or disproven. It is the organized
process of determining the accuracy of scientific concepts.
The scientific method is a series of steps followed by scientific investigations to answer specific questions about the natural world.
It involves making observations, formulating a hypothesis and conducting scientific experiments. Scientific inquiry starts with an
observation followed by the formulation of a question about what has been observed.
Steps of the scientific method
The steps of scientific methods are as follows:
Experiment: to support, refute or validate a hypothesis
Define purpose (idea): I want to know if water freezes faster on its own or with sugar added.
Construct hypothesis: Will water freeze faster or slower with the addition of sugar?
Test of the hypothesis and data collection: Place two containers of equal amounts of water, one with sugar added, into the freezer.
- At intervals of 30 minutes, open the freezer to determine the status of each container.
- Continue until both have frozen. - Write down the times that the containers were checked and when they each
reached a fully frozen level.Analyze data
Review the dataDraw conclusion
Decide: Did water freeze faster or slower with the addition of sugar?Communicate results: Report findings either verbally (Communication) or in
Writing for Science Subjects: Characteristics of Scientific Writing
Scientific writing follows these conventions:
It is conventionalIt is clearIt is conciseIt is accurate (precise)It uses formal languageIt is objectiveIt exercises caution (vigilance, care)It avoids direct quotesIt gets to the pointIt is often illustrated with figures
1. It is conventionalThis means that scientific writing follows strict rules, with regard to a number of issues:
- Structure:Aarticles in scientific journals are usually arranged under a series of headings. Here is a
typical structure for a report on an experiment, with suggestions for the kind of information that should be included in each section. It is crucial when writing reports that
you should include your information in the correct section:
1. Aim: Describe the purpose of the experiment 2. Abstract: Give a short summary of the whole report, including conclusions
3. Method: Describe the techniques and materials you used. Discuss any difficulties in carrying out
the experiment 4. Results: Describe your observations. Include calculations where appropriate 5. Discussion: Critically evaluate the significance of your results. Compare with
previous studies. Discuss weaknesses in your study and suggest future avenues for investigation
- Use of abbreviations- The use of abbreviations is common in scientific writing, especially for long
technical terms and it can be a way to make your writing flow more smoothly.- Always give the term in full at the first use and show the abbreviation in
- Formatting of names, technical terms etc.- Every discipline has its own conventions - for chemical elements and compounds,
nuclear particles and so on - and it is important that you know those in your subject.- Refer to your lecture notes and text books or try the style manual in the resources
- Use of tenses- Different tenses are used for writing about different types of information and in
different sections of a scientific report:
- Referencing - You must reference fully and accurately, according to the required style.
2. It is clear- One idea per sentence
- One theme per paragraph
3. It is concise- Use as few words as possible e.g. “now” instead of “at the present time”;
“near“ instead of “in close proximity to” - Avoid repetition within sentences as repetition just makes the sentence
more confusing because everything is repeated unnecessarily and this repetition reduces clarity and flow (because it’s repetitious).
4. It is accurate- Use simple terms e.g. “identical” instead of “exactly identical”
- Avoid vague terms like “most”, “nearly”, eg “The concentration was tested every 15 minutes” instead of “The concentration was tested regularly”.- Avoid over generalization e.g. “it is widely accepted”, not “everyone
5. It uses formal language- No contractions (“do not” instead of “dont”)
- No colloquialisms/ conversational terms ( “children” not “kids”).- Be accurate rather than polite! E.g. “Man/Woman” not “Gentleman/ Lady”.
- No rhetorical questions e.g. “So, what do these results mean?”- Try to write in an active style rather than passive.
6. It is objective- You should avoid expressing your unsupported thoughts or beliefs – any
opinion you give or claim you make must be supported by appropriate evidence - You should aim to write as a neutral outside observer, without any emotional or
personal investment in the subject
7. It exercises cautionThis also relates to accuracy – in scientific writing it is important to write
exactly what you mean.- Take care not to overstate what your evidence can support.
- Be especially careful with words like “proves” or “definitively”.
8. It avoids direct quotes- You would only use a direct quote (citation directe) from a source when the
exact words used by the author are essential to make your point.- In writing for science this situation is very rare because it is the ideas that
matter most.- Explaining the ideas in your own words better demonstrates your
understanding of the issue (of course, you still have to cite the source!).
9. It gets to the pointMore than any other form of writing, scientific writing is skimmed or scanned – if
the reader can’t see the point of your work in about 30 seconds, they probably won’t read it at all!
10. It is often illustrated with figures
- Tables, graphs, charts, photographs etc. - All figures must be good quality reproductions and clearly readable/visible.
- Keep it as simple as possible. Dont, for example, plot ten sets of data on the same graph.
- Represent each set of data in only one illustration. Figures must be clearly labeled.
- Give each one a brief, descriptive title.- Each figure should have a legend which briefly describes the experiment and tells
the reader what they are looking at.- The key points of the illustration should be discussed in the main text.
Writing for Science Subjects: characteristics of scientific writing
“I am going to talk about the idea of progress. Foremost, I would like to giveyou a definition of this notion : Progress is a positive evolution that can varyaccording to time and events. There is scientific progress, social, political,technical, intellectual etc. However, the idea of progress is still debatebetween those who consider that it’s beneficial and those for whom it’sharmful. So, it is interesting to wonder : To what extent does progress havean impact on our society ? We will see that progress can be detrimentalparticularly at the level of environment, but it can be essential to evolve”,