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:
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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.
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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.
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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:
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.
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