Error Margins
4
5.1 Introduction
EMBN
When rounding off, wethrow away some of thedigits of a number. Thismeans that we are making an
error. In this chapter wediscuss how errors cangrow larger than expected if we are not carefulwith
algebraic calculations.
See introductory video:VMefg at http://www.everythingmaths.co.za4.2 Rounding Off
We have seen that numbers are either rational orirrational and we have see how to round off numbers.
However, in a calculation that has many steps, itis best to leave the rounding off right until the end.
For example, if you were asked to write
3√
3 +
√
12
as a decimal number correct to two decimal places, there are two waysof doing this as described in
Table 4.1.Table 4.1: Two methodsof writing 3√
3 +
√
12 as a decimal number.
�Method 1 �Method 2
3√
3 +
√
12 = 3
√
3 +
√
4. 3 3
√
3 +
√
12 = 3× 1 ,73 + 3, 46
= 3
√
3 + 2
√
3 = 5,19 + 3, 46
= 5
√
3 = 8, 65
= 5× 1 , 732050808...
= 8, 660254038...
= 8, 66
In the example we see that Method 1 gives 8 , 66 as an answer while Method 2 gives 8 , 65 as an answer.
The answer of Method 1is more accurate because the expression was simplified as much as possible
before the answer was rounded-off.
In general, it is best tosimplify any expressionas much as possible, before using your calculator to
work out the answer indecimal notation.TipIt is best to simplify all
expressions as much as
possible before round-
ing off answers. This
maintains the accuracy
of your answer.