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Approximation Correction

Aim:
This exercise is to help you to avoid common mistakes in the use of the language of approximation that students make in report writing assignments. (This page is also available as a MS Word document.)

Introduction:
In report writing it is good style to use 'approximation' in the Findings, Conclusions and Recommendations. Approximation means describing numbers or statistics by using a fraction that is similar to the exact number; e.g. using 'about one-third' instead of 34.76%, or an easy-to-remember number such as 'just under one million' instead of '997,652'.

There are a number of reasons for doing this. Firstly, it is easier for people to understand and remember. Secondly, the numbers or statistics may be more detailed than necessary.

Here are some examples:

65% about two-thirds of   1,043 over a thousand
28% just over a quarter of 115 over a hundred
21% about a fifth 9 fewer than ten
49% just under a half of 2 a small number
74% almost three-quarters of 4 a few
33.3333% a third of 6 several
92% most of 749,982 about three-quarters of a million
98.5% almost all 1,256,890,534 over 1.2 billion

Tips:

  • don't use fractions where the denominator (the number under the line) is greater than 5 - many people do not know that 1/6 = 16% or that  7/8 = 87.5%
  • don't forget the hyphen in fractions; e.g. 'one-third' (but not after 'a'; e.g. use 'a third')
  • don't forget to add an 's' on the end of fractions starting with two or greater; e.g. 'two-thirds', 'three-quarters'
  • most fractions can be followed by the preposition 'of '; e.g. 'Three-quarters of the staff were satisfied with working conditions.'
  • most fractions are followed by a plural noun; e.g. 'half of the books', except uncountable nouns; e.g. 'Half of the staff were satisfied with working conditions' (the verb is 'were', not 'was', because 'staff ' is thought of as a plural after fractions)
  • in strictly correct grammar use 'fewer than' for countable nouns and 'less than' for uncountable nouns
  • it is more natural to use 'a' instead of 'one' in front of fractions; e.g. 'a third of ...'
  • in front of 'half ' you do not need to use 'a' or 'one-'; e.g. 'Half of the staff were satisfied with their working relationships.'
  • do not use a number at the start of a sentence, because it's bad style. Use words; e.g. '100 One hundred of the staff were satisfied with working conditions.'
  • be careful of the spelling of 'several' - it's not 'serveral'
  • remember that 'only' and 'just' often have a negative meanings, so use them only if you want to show that something is bad; e.g. 'Only 1% of our staff were satisfied with working conditions.'

Instructions:
Correct the errors in the following sentences. There may be more than one error in each sentence.











 

 

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Answer

Your answer

Model answer
Two-thirds of the staff was were happy with their bonus.

Explanation
Most fractions are followed by a plural noun; e.g. 'half of the books', except uncountable nouns; e.g. 'Half of the staff were satisfied with working conditions' (the verb is 'were', not 'was', because 'staff ' is thought of as a plural after fractions).

Your answer

Model answer
'Nearly 20% of the staff went home early.' or 'Sixteen percent of the staff went home early.' etc. ('Sixteen percent' is acceptable because there is no fraction that accurately but also approximately describes it) Don't use 'One-sixth', 'One sixth' or 'A sixth' .

Explanation
Don't use fractions where the denominator (the number under the line) is greater than 5 - many people do not know that 1/6 = 16%.

Your answer

Model answer
Regarding the training opportunities, about half of the staff said that they were satisfied.

Explanation
'Just' and 'only' often have a negative meanings, so use them only if you want to show that something is bad; e.g. 'Only 1% of our staff were satisfied with working conditions.'

Your answer

Model answer
Opportunities for promotion were important to several staff.

Explanation
Be careful of the spelling of 'several' - it's not 'serveral'

Your answer

Model answer
Two-fifths of respondents are satisfied with the opportunities for promotion.

Explanation
Don't forget to add an 's' on the end of fractions starting with two or greater; e.g. 'two-thirds', 'three-quarters'

Your answer

Model answer
Less Fewer than 30 replies were received.

Explanation
In strictly correct grammar use 'fewer than' for countable nouns and 'less than' for uncountable nouns

Your answer

Model answer
Three-quarters of  the test subjects did not understand Question Ten.

Explanation
Don't forget the hyphen in fractions.

Your answer

Model answer
Only a quarter of the test subjects completed the task successfully.

Explanation
It is more natural to use 'a' instead of 'one' in front of fractions.

Your answer

Model answer
The population of Hong Kong is about 6.7 million.

Explanation
The number 6,732,129 is not an approximation, it is too detailed.

Your answer

Model answer
106 Just over a hundred people replied to the questionnaire.

Explanation
Do not use a number at the start of a sentence, because it's bad style. Use words; e.g. '100 One hundred of the staff were satisfied with working conditions.'

 

Last updated on: Monday, March 26, 2012