Week 7 Overview – ‘Rounding, significant figures & units’
As we move closer and closer towards the exam, my advice to students would be to begin working through practice exams made by external companies and past papers from VCAA. Hopefully people have completed their bound references and can use them whilst working through practice papers.
These are recommendations and not everyone learns in the same way, so take all advice with a grain of salt.
Rounding is involved in majority of Further Maths exam questions, so it is important to get it right.
The general rule is:
1. ‘0 – 4’ round down
2. ‘5 – 9’ round up
E.g. 3.256 rounded to one decimal places
= 3.3 as ‘.25’ rounds up to ‘.3’
Typically, in a Further Maths exam, one if not more questions will ask students to round to a level of ‘significant figures’.
The general rule for Significant figures:
1. Any non-zero digit is SIGNIFICANT
2. Zero’s between non-zero digits are SIGNIFCANT
3. Trailing zero’s in decimals are SIGNIFICANT
The general rule for Non-Significant figures:
1. Leading zero’s in decimals are NOT SIGNIFICANT
2. Trailing zero’s in whole numbers are NOT SIGNIFICANT
E.g. 170.0043 = 7 significant figures
E.g. 0.0043 = 2 significant figures
E.g. 0.00430 = 3 significant figures
E.g. 170 = 2 significant figures
This goes without really saying; if a question involves any sort of units, use the units in all answers related to the question.
Don’t miss simple marks as you didn’t write cm, km, hours etc.
Common Sense Units
‘Common sense units’ apply when an examiner doesn’t specifically detail how many decimal places are required in an answer. In Further Maths, if a question does not detail the number of decimal places required; we usually assume 2 decimal places however if the context of the question means 2 decimal places does not make sense, we apply ‘common sense units’ which requires students to round down to the nearest whole number.
E.g. If the question asks how many people were at the event, and your answer is 4.56 people, you should round down to 4 people, unless otherwise specified.
This is because we have 4 full people that have evidently attended the event, we do not have 5 people in attendance, nor do we have 4.56 people in attendance as this is impossible (cannot have .56 of a person).
I do doubt that there will be a situation where the application of ‘common sense units’ is necessary on your exam. However, why not be prepared just in case?
This week we went through rounding, significant figures and units. I hope these examples are helpful for students going forward with their revision programs.
See you next week.