Rounding
Introduction
As examples, you might be asked to

In everyday life, distances are commonly quoted to the nearest kilometre, or whatever  they are not usually quoted precisely, except in rare cases.
For example, if the distance between two points is stated as 9 kilometres, then you might possibly expect that the real distance could be anywhere between 8.5 kilometres and 9.5 kilometres.

Margot Is egg production going OK. How many did you have today ? Tom About two dozen Barbara I collected 22 this morning Tom That's about two dozen, isn't it ? Barbara Well, no it isn't if you want to be precise, no it isn't. Tom I wasn't being precise. Remember, I said about two dozen. Barbara Then why are you making such a big issue about it, then ? 


A pedant writes 
Rounding to the Nearest Whole Number
For example,
 the number 29.345 will be rounded to 29
 the number 29.654 will be rounded to 30
The important feature is the first decimal place.

So all the following numbers will become 25
 24.5
 24.513
 24.769
 24.976543
 25.034
 25.3
 25.476
 the first decimal place is all that needs to be considered.
Round these numbers to the nearest whole number a) 34.65 b) 234.789 c) 12.3469 d) 12.3 e) 345.5 
Rounding to the Nearest Ten
This, as for all rounding, employs a procedure analogous to that used for rounding to whole numbers.
For example,

The important feature in this case is the first "ignored" number.

Round these numbers to the nearest ten a) 34.65 b) 2349 c) 124.69 d) 12.3 e) 3467 f) 23452 
Rounding to the Nearest Hundred, Thousand.. etc.
For example,

The important feature in this case is the first "ignored" number.

Round these numbers to the nearest hundred a) 346.5 b) 2349 c) 1473.9 d) 1234.3 e) 3467 f) 23821 and these to the nearest thousand g) 3895 h) 2426 i) 5473.9 j) 52343 k) 32766 l) 345821 and these to the nearest million m) 8 378 723 n) 45 983 233 
The crowd at a fotball match is given as 34,700 to the nearest hundred. What is the largest number and lowest number of spectators that could actually have attended ? 
Rounding to the Nearest 0.1 (Rounding to One Decimal Place)
For example,

Note the similarity with the previous methods of rounding.
Round these numbers to the nearest 0.1 a) 32.3492 b) 2034.234 c) 526.682 d) 12.034 e) 46.873 f) 23.52 
Rounding to a number of Decimal Places
Rounding so that there is one figure to the right of the decimal point is called
Rounding so that there are two figures to the right of the decimal point is called
and so on, by analogy.
Example
234.5854
rounded to 1 decimal figure  : 234.6 
rounded to 2 decimal figures  : 234.59 
rounded to 3 decimal figures  : 234.585 
Example
rounded to one decimal place would be
Significant Figures
A number which has been rounded to the first nonzero figure has been rounded to one significant figure. For example
132  100 
0.00249  0.002 
By analogy, rounding to 2 significant figures produces
132  130 
0.00249  0.0025 
Note that when displaying numbers to a certain number of significant figures, any leading zeros are not taken into account. For example,
rounded to 2 significant figures is
However, trailing zeroes are taken into account. For example,
rounded to 3 significant figures is
and
rounded to 2 significant figures is
Important When doing calculations, your answer should not be given to a greater number of significant figures than the least number of significant figures used in your input data
For example, if your input data was 20.3, 9.2 and 3098, your answer could only be quoted to two significant figures (becasue of the two significant figures in 9.2)

Necessary and Unnecessary Zeros
For numbers which contain nonzero figures to the right of the decimal point, any trailing zeros are superfluous, unless they are significant figures.
For example
3.970 = 3.97
but to four significant figures
and
Zeros obviously cannot be dispensed with when they are needed to 'keep a place'.
For example, zeros cannot be dispensed with in the following numbers
5000
When a number is less than 1 and greater than 1, you have a choice as to how to present it. A number like
It is a matter of personal preference, although the former is probably more common.
Examples
The marchers formed a milelong procession Fifteen thousand people took part in a march through the streets of London in protest at university fees. The National Union of Students rally was calling for the abolition of the £1,050 annual tuition fee and opposing the introduction of "topup" fees which could cost up to £4,500 a year. The march  part of the union's Winning for Students campaign  started out from the University of London and finished in Kennington Park, South London. 
30,000 people are expected to run in a race which has become a fixture in the nation's calendar since 1981. Such is the status of the event that half a million people will be in attendance to cheer on the competitors, while it is expected that the race will be televised to over 100 countries around the world. The first London Marathon was run on March 29 1981. Incredibly, the number of applicants for the race  20,000  was smaller than the number that will actually run this Sunday. With the amount of competitors increasing every year, more money will be raised this Sunday than during previous races. It is estimated that in the 18 year history of the event, £ 80m has been raised. At 42 kilometers, starting at Greenwich Park and finishing by The Mall, the race itself is a gruelling test of endurance and stamina. 15,000 runners pull out during the months preceding the race for a variety of reasons, including lack of appropriate fitness and health concerns. Additional events now form the day that is the London Marathon. A mini marathon is run for 2,000 children between the ages of 1117. 
......by 1626 there were 4,000 soldiers quartered at Portsmouth. ...... one thousand dockyard men emigrated to Canada during the period of 186970. ......bombing in World War II virtually destroyed some areas of the City. The Dockyard was devastated. In 1945 there was a workforce of 45,000. ......there was further decline in the 1980s resulting from Defence Reviews. In July 1981 Parliament confirmed the rundown of the Dockyard by reducing the labour force from 7,200 to 1,200. The current workforce is 1700. 
 
* Paris  Alençon  195 km 
* Caen  Cherbourg 
120 km  
* Paris  Caen  240 km 
* Deauville  Alençon  120 km  
* Paris  Cherbourg 
360 km  * Deauville  Rouen 
90 km  
* Paris  Dieppe  195 km 
* Rouen  Dieppe  60 km  
* Paris  Mt St Michel 
325 km 
* Rouen  Le Havre 
85 km  
* Paris  Rouen  140 km 
* Rouen  Mt St Michel 
255 km 
Past Exam Questions
1. A pop concert has an audience of 8 496 people. Two thirds of the people at the concert pay a £15 entrance fee while the remainder pay a reduced rate of £7. What is the income from the concert to the nearest thousand pounds?
 A £80 000
 B £82 000
 C £104 800
 D £105 000