In the previous blog, in which I calculated the arc length of the Clifton Suspension Bridge, there were multiple steps to solving the problem. We had to calculate the radius of the sector. Then, we used this radius to calculate the angle of the sector. Then we had to use both of these numbers to find the arc length.
We calculated the radius as 233.17307692 metres. We must make sure that we use this exact number in the later calculations too, however tempting it may be to just round it to 233.2 or even 233. In this blog, I’ll explain why we need to do this by using another simpler example involving algebraic substitution. This is a very common mistake that is made by students and can lead to unnecessary marks being lost.
Example question
B = A2
C = 5B
Find C when A = 3.44, giving your answer to the nearest integer.
Incorrect solution
B = 3.442 = 11.8336 = 12 (to the nearest integer)
C = 5 × 12 = 60
This answer is nearly right, but it’s not quite right. The mistake I made was I rounded the 11.8336 to the nearest integer and then used that rounded answer to find C. We should only round the final answer to the nearest integer. We should not do any rounding after any previous calculations. Look what happens when we do things correctly.
Correct solution
B = 3.442 = 11.8336
C = 5 × 11.8336 = 59.168 = 59 (to the nearest integer)
So this time, we ended up with 59, which is the correct answer.
When we calculated C, we used the full value of B (11.8336) instead of the rounded value (12).
So, you see how we got the answer slightly wrong because of the rounding error. To avoid this, make sure you only round at the end of the question – not at any previous steps.
If you need to practice rounding, try our rounding worksheet. Likewise, if you need to practice algebraic substitution, you can try our substitution worksheet.
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