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1.1 –8 ; 12 ; 5–11 ; 4 + 0 – ; ; ; ; ;
1.2 2.5 – ½ ; ; ; ; 0,5 ; 0,05 ; 0,005
1.3 3 ; 3,5 ; 3,14 ; 22 7 ; 355 113 ;
end of GROUP ASSIGNMENT
CLASS WORK
1 Of course one can write any number in many ways:
1.1 Is 1 3 equal to ? What about ? And 1,33 of 1,333 of 1,3?
1.2 Is the same as 2,2? Or 2,24? Or 2,236? Or 2,2361? Or maybe 2,2360? Discuss.
1.3 Is 3 and 3,5 and 3,14 and 22 ÷ 7 and 355 ÷ 113 the same as ? Make a decision.
2 We can’t always write 3,1415926535897932384626 . . . when we want to use. Why not?
If I have to write down exactly what is, then I must write ! The others in question 1.3 are only approximately equal to. But when I have to use in a calculation to get an answer, then I have to be able to round off properly.
This is π rounded off to different degrees of accuracy :
1 decimal place: 3,1
2 decimal places: 3,14
3 decimal places: 3,142
4 decimal places: 3,1416
5 decimal places: 3,14159
6 decimal places: 3,141593
3 Simplify and round off the following values, accurate to the number of decimal places given in the brackets.
3.1 3,1 3 (2)
3.2 2 × 2)
3.3 5 × (2)
3.4 4,5 × (0)
3.5 1,000008 + 25 10000 (1)
end of CLASS WORK
How many seconds in a century?
CLASS WORK
1.1 How many hours are there in 17 weeks? 24 × 7 × 17 = 2 856 hours
1.2 How many minutes in a week? 60 × 24 × 7 = 10 080 minutes
1.3 Is it just as easy to calculate how many hours there are in 135 months? Discuss the question in a group and decide which questions have to be answered before the answer can be calculated.
1.4 How many years are there in 173 months? 173 12 = 14,4166 ≈ 14,42 years
2 Why do we multiply in question 1.1 and 1.2, and divide in question 1.4?
3 How many seconds in a century? It may take a while to get to the answer! How will you know that you can trust your answer?
4.1 There are one thousand metres in a kilometre, so we can say that one metre equals 0,001 kilometres. One metre = 1 1000 kilometres or 1 m =
4.2 There are one thousand millimetres in a metre: 1 mm = = 0,000 001 km
4.3 There are one thousand micrometres in a millimetre: 1 μm = 0,000 000 001 km. (μ is a Greek letter – mu.)
5 Just as we can write very large numbers more conveniently in scientific notation , we also write very small numbers in scientific notation. Below are a few examples of each. Make sure that you can convert ordinary numbers to scientific notation, and vice versa. Calculators also use a sort of scientific notation. They differ, and so you have to make yourself familiar with the way your calculator handles very large and very small numbers.
5.1 1 μm = 0,000 000 001 km So: 1 μm = 1,0 × 10 –9 km
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