### Chapter 3: An Introduction to Approximation and Estimation

Source: My Paper Friday August 8, 2008

In the above newspaper cutting, some figures are exact, some are approximated figures.

Do you know why sometimes exact figures are used, while sometimes approximated figures are used?

From the above newspaper cutting,
(a) Identify one information where exact figure is used, and why you think the exact figure is used.
(b) Identify one information where approximated figure is used, and why you think an approximated instead of exact figure is used?

1. a) 28 sports. Because 28 is still a counting number and easy to calculate.
b) 10m Bicycles. It is not possible that 10m bicycles could be counted so it should be estimated.

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3. Exact: 28 Sports.
Approximated: 10000 Bicycles

4. 28 sports because we must know how many sports exactly as each sport is important.
5000 yuan because it is just to show this event is very expensive.

5. 10,000,000 Bicycles: Approximated figure as Beijing cannot possibly count exactly the amount of bicycles it has.

30 Yuan: Exact, as they set the cost of the ticket so it must be true.

6. 5000 yuan for cost for opening ceremony is exact value.
10 000 000 bicycles in beijing is approximated

7. (a) 16 days from opening to closing ceremony. It is exact because the amount of time it goes on for is important, so it is exact.
(b) 10,000,000 bicycles in beijing. It is not very important, so it is an approximate.

8. a)302 medal events exact because it is a record
b)10,000,000 bicycles approximated as the other numbers are not important

9. A) 28 sports It is a easy-to-count
B) 120 billion yuan It cannot be so likely that it is a exact figure

10. a) Quote "198km train track in Beijing by 2008" (Exact Figure)
It is probably because it is a permanent thing and also because it is rather significant. (Concerning the country)
b) Quote "10,000,000 bicycles in Beijing" (Approximated figure)
Bicycles are being produced every single day and thus, we do not have the exact figures. Even if we were to count the exact figures, probably in the next 5 minutes, the total bikes would change and so it would be ridiculous to count in exact figures so they rounded off to a approximate figure.

11. (a)28 sports is a exact number as a sport cannot have decimal so it is like eg. there are 28 sports >estimated = 30 sports so they can just put 28 sports.
(b)16,330,000 permanent residents as there are so many residents it is impossible to count them one by one so they are most probably approximated figure.

12. a) 28 sports, this is an exact figure as its last digit is not a 0
b)100000 volunteers is an approximated figure as it could be a rounded-up of the real number.
JiaEn

13. 302 gold medal events
2,500,000 expected visitors during the games.

14. (a) The 302 gold medal events is exact as they are very important as if they use an approximate figure, people will think that there are more medals awarded than the actual figure.

(b) The 16 330 000 permanent residents of the city is and approximated figure as there are just too many residents to count and that is not really an important figure as compared to the others.

15. 7000000 tickets
28 sports

16. exact-16 days to closing ceremony. This is because they are counting down, thus they have to be accurate as they are informing the public of the remaining days.
approximate-Beiging has 10 million bicycles. This is a estimate or it would not be a number without any others instead of zeros.

17. Hope i am earlier to post
a) 28 sports
b) 16330000 permanent residents of the city (2007)This is not possible as they can't possibly update the number every second as a lot of permanent resident that will give birth so u can't possibly count all every second

18. a) 28 Sports
b) 10,000,000 Bicycles

19. 302 gold medals to show exact number of winners of athletes

16330000 approximated to show overall number of people living in China

20. Exact: 16 days from opening to closing cermony.

Approximated: 10 000 000 bicycles in Beijing.

21. a) I think that the exact figure is the "from opening to closing days", as the number is very small and it can be easily counted.

b) I think that the approximated figure is the numbers of bicycles in beijing, as they cannot possibly count so many of them

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23. The approximated number of visitors to Bejing during games is 2,500,000.I think this is an approximated value as the exact number of people would not come.

The number of sports which is 28 is exact as it is easy to count.

24. a) 16 days between the end and the start of the games. The number of days between the start and the end of the games can be exact because it can be easily counted.

b) 5850000 tonnes of rubbish produced. The exact number of rubbish produced is impossible to calculate.

25. Good reasoning, S1-02 :)

@Kashyap:
You may want to re-consider "5000 yuan for cost for opening ceremony is exact value." Do you know why?

@Matt:
This is an interesting one - which could be either exact or approximated unless we have background information.
Quote "198km train track in Beijing by 2008" (Exact Figure). It is probably because it is a permanent thing and also because it is rather significant. (Concerning the country)
But you are basically correct as it's significant. However, we also would not eliminate the fact that it might be only "197.5km" or other values close to "198km".

@Matthew @Leighton @Christabel: You have not put down reasons why you think the figures are exact/ approxiated.