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Approximation methods

15.79 is 16 to the nearest whole number.
3,125 is 3,100 to the nearest hundred.
Two special approximation methods are used in mathematics: decimal places (d.p.) and significant figures (s.f.).


Decimal places (d.p.)

Statements such as "there are five pencils in the box" are considered exact because the pencils can be counted. In a statement like "the planet Pluto, at it's closest point is 4,250,000,000 kilometres from Earth" an exact number is not required and a rounded number is used.
The first digit to be discarded is called the key digit.


Important rules:

  • if the key digit is less than 5 round down.
Examples:

6.3534 is 6.353 to three d.p.
7.0135 is 7.01 to two d.p.
8.430 is 8.4 to one d.p.

  • if the key digit is greater than 5, or if it is a five followed by digits other than zero, round up.
Examples:

5.41483 is 5.415 to three d.p.
6.2673 is 6.27 to two d.p.
7.98 is 8.0 to one d.p.

  • if the key digit is 5, followed only by zeros, round to the nearest even digit.
Examples:

4.7500 is 4.8 to one d.p.
1.2650 is 1.26 to two d.p.


Exercise 1

Round off to three decimal places:

a)  6.135135

Solution:
6.135135 is 6.135 to three decimal places because the key digit in our case is 1, which is less than 5 and therefore we round down.

b)  0.424721 is 
c)  1.045456 is 
d)  33.46551 is 
e)  43.36452 is 
f)  8.006025 is 
g)  321.325425 is 
h)  2.22452 is 
i)  15.93754 is 
j)  0.050625 is