There are three main ways to round numbers:
(i)  to the nearest 10, 100, 1000, etc; 

(ii)  to a certain number of significant figures; 
(iii)  to a certain number of decimal places. 
Note that a measured length such as '12 cm to the nearest cm' means that the actual length lies between 11.5 cm and 12.5 cm.
By convention, we normally round 0.5 up to the next whole number, so in fact,
11.5 cm ≤ actual length < 12.5 cm
We call 11.5 the lower bound and 12.5 the upper bound. We can also write the upper bound as
12.4999 . . . . or 12.49
where the dot above the 9 means that it is repeated indefinitely, or recurs.
It is important to see that 12.49 is not the upper bound, as, for example, the length could have been 12.498.
A football match is watched by 56 742 people. Write this number correct to the nearest,
(a)  10 000, 
60 000


(b)  1000, 
57 000

(c)  10. 
56 740

Write each of the following numbers correct to 3 significant figures:
(a)  47 316 
47 300


(b)  303 971 
304 000

(c)  20.453 
20.5

(d)  0.004368 
0.00437

Write each of the following numbers correct to the number of decimal places stated:
(a)  0.3741 to 2 d.p. 
0.37


(b)  3.8451 to 2 d.p. 
3.85

(c)  142.8315 to 1 d.p. 
142.8

(d)  0.000851 to 4 d.p. 
0.0009

State the upper and lower bounds for each of the following quantities and write an inequality for the actual value in each case.
4 mm to the nearest mm.
Upper bound = 4.5 mm
Lower bound = 3.5 mm
3.5 mm ≤ actual value < 4.5 mm
15 kg to the nearest kg.
Upper bound = 15.5 kg
Lower bound = 14.5 kg
14.5 kg ≤ actual value < 15.5 kg
4.56 m to the nearest cm.
Upper bound = 4.565 mm
Lower bound = 4.555 mm
4.555 m ≤ actual value < 4.565 m