### 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) 16 days from the opening ceremony to the closing ceremony. The people want to know exactly how many days the games last. Hence, it should be an exact figure.

b)5 850 000 tons of rubbish were produced in the city in 2006. The people do not really want to know the exact amount of rubbish as they just need a number large enough to shock them.

2. a) 28 sports people want to know how many sports are there as all the sports are unique.
b) 7,000,000 tickets sold - the public wants to know how many tickets have been sold but do not know the exact figure as one or two more people do not make a difference.

3. a) 28 sports as it is an important piece of information to the people watching the beijing olympics.
b) 10,000,000 bicycles in BeiJing . It is not possible to count the exact number of bicycles . So , it is most probably approximated.

4. a) 28 sports. There is no need to approximate this figure as it is a very small number.

b) 25,000,000 expected visitors to Beijing during Games. As it is only expected, it is very unlikely to know the exact figure of the number of figures visiting Beijing.

5. a)16 days from the opening to closing ceremony.The public would want to know how long the Beijing Olympics would last.

b)302 gold medal events.The athletics would want to aim for the gold medals and they can count how many are left to be won by their country so, it is important to state the exact no. of gold medals.

6. a)28 sports is the exact figure.People wants to know how many types of games are there.

b)10000000 is a approximate figure.People would not care about the extra digit that is small and would not change the fact much

7. a) 16 days from opening to closing ceremony. It is important for people to know the exact day where it will end

b) 10000000 bicycles in BeiJing. Impossible to find exact number

8. a)28 sports. if it were to be rounded of, people will actually think that it is the Actual number when its not. therefore, to avoid confusion,it should be an exact figure.

b)120 billion yuan. as it is a massive amount of money, it will take a lot of time to count every dollar bit by bit. therefore, it is simplified by just rounding of the amount of money.

BTWFYI I am you-know-who (Ishani)

9. a) 28 sports and 205 nations competing.It is because every single one more nation taking part in the games or sport event will make a big difference

b)16330000 PRs in Singapore,one more PR would not make a significant difference to the whole population of PRs

10. a) 302 gold medal events is exact.Since this is a international people will want to compare with other countries and also since all the medals are recorded so they use exact figures
b)10000 bicycles are approximate.The number of bicycles are very large so if they use exact it should not even be possible ,so they use approximate.
-Ruoyu

11. (a) 302 gold medal events. The spectators will want to know how many gold medal events there are, so it should be accurate.

(b) 120 billion yuan invested in the event. The government might have invested more or less than that amount, but in this case it doesn't really matter, and it would be hard to calculate how much they invested, so it should be approximated.

12. Mark :) :( :&#39;( (^^^) :D :O :42: O:) :p 3:)3/01/2011 12:15:00 PM

(a) 198km is an exact figure. This is because it is a world record and every kilometer matters.

(b) 5,850,000 is an approximate number. The people cannot and will not give the exact number of rubbish because the detailed numbers do not make any significant difference. Also, the number of rubbish is always increasing

b)400,000 city volunteers.It is not so important to know how many city volunteers are there so it is easier to post the estimated amount.

14. a) 28 sports is an exact figure. I say this as 28 is not needed to be rounded up or down.

b) 120 billion yuan is an approximate figure. I say this as the country needs to approximate the net profit or the increase in the country's economy.

15. a) 16 days to the closing ceremony. To let people know how long will the olympic be held. People would want to watch the closing ceremony as the opening ceremony was very magnificent and breathtaking, so they would be anticipating if the closing ceremony.
b) 65000. People will not be interested in the number of buses people took to attend the games.

16. a) 28 sports. The people will want to know how many sports are played during the games so that they will know what games will they watch.

b)16,330,000 permanent residents. They are not able to count all the residents in the country as it is very big and is impossible.

17. a)28 sports. 28 is a small number and they can count it easily.
b)7000000 tickets sold. There are a large number of tickets sold so they just round off the number to 1 significant figure.

18. a) Exact Figures

Eg: 28 sports in the Beijing Games.
The people who are watching the games want to know about the exact number of sports played as this is significant .The number 28 cannot be rounded up .

b) Approximated Figures

Eg: 10500 athletes competing in the Games.
The number of athletes competing is too many to be exact so they round up the number to a whole. This number is not very important for people to know the exact figures

19. a) 30 yuan is exact as the people would want the amount of money needed exact to participate

b) 5850000 tons of rubbish are approximated as the ton must be decimal.Also the readers also want to infer more easier and would not care the exact number

20. a) 30 sports. People want to know the exact admission fees for the softball preliminaries, thus it should be exact.

b) 3, 300, 000 forecast number of cars in Beijing by time of games. There are too many cars, thus the number should be approximated as it is impossible to count them one-by-one.

Nina

21. 28 sports. People want to know how many sports are going to be participated in.
10000000 bicycles in beijing. It is impossible to find an exact figure, so it has to be estimated.

22. BTWFYL, Nemo is Owen

23. a)302 gold medal events is an exact figure. The number is not very huge and the gold medal is very important, so people want to know it. So it must be an exact figure.
b)100000 official Olympic and Paralympics volunteers is an approximated number. There is a lot of people and people may be constantly joining and leaving, so the number cannot be confirmed.