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The headlines above are fairly typical of what we might see in the newspapers. Numbers
are ‘rounded’ rather than giving the exact number. Why does this happen?
• The actual number is not known so an estimate is given.
• There’s no real need to know the exact number - the job of the headline is to give
instant meaning and rounded numbers have more impact.
• The numbers concerned are very large so tens or even hundreds either way don’t make
much difference.
We use estimates and rounding all the time even though we might not realise it. Here are
some examples:
• The train journey takes 53 minutes so we think of it as an hour.
• It’s about 100 miles from here to London - it may actually be 92 or 105.
• Lunch from Monday to Friday costs around £3.75 a day which is about £20 per week.
• Buying the T shirt for £5.99 and the trousers for £12.99 means I can get them both for
under £20.
• There are six people eating; most eat three roast potatoes, so I’ll do 20.
Give it a try: Start looking out for numbers in newspapers and on the news. Consider what
you do on a daily basis and ask yourself:
• How accurate is the number?
• Is it an approximation?
• Could anyone know the actual number?
• Is it an estimate?
• Is it ‘good enough’?
If each member of boyband
One Direction tweets 10
times in one hour, how mant
tweets do One Direction
make in a week
Mathematical rounding
Mathematical rounding means something specific; it’s not just giving a rough idea or
approximation. There is a rule for rounding when you do mathematical calculations and it’s
this:
If the last digit to be considered is 5 or above then round up, otherwise round down.
This is best shown by examples:
Let’s take 4,572 (which we say as four thousand, five hundred and seventy–two) and see
what happens:
• 4,572 to the nearest 10 is ……4,570 (2 is less than 5 so we round down)
• 4,572 to the nearest 100 is …..4,600 (7 is more than 5 so we round up to the next 100)
• 4,572 to the nearest 1,000 is …5,000 (5 is 5 or above so we round up to the next
1000)
Try these:
• 7,285 to the nearest 10 is ………………
• 7,285 to the nearest 100 is ……………..
• 7,285 to the nearest 1,000 is ……………
And these:
• 63 to the nearest 10 is …………………
• 1,257 to the nearest 100 is …………….
• 7,499 to the nearest 1,000 is …………...
• 5,782,299 to the nearest 100,000 is ….
Now try these: (why not highlight the digit you need to consider to help you)
• 3,255 to the nearest 100 is …………………
• 2,067 to the nearest 100 is …………….
• 7,009 to the nearest 10 is …………...
• 299 to the nearest 10 is ….
7,290
7,300
7,000
60
1,300
7,000
5,800,000
3,300
2,100
7,010
300
What about these?
At the factory where you work, daily production figures are given exactly, weekly
production figures are given to the nearest 10 and monthly production figures are given to
the nearest 100.
You are presenting production figures to your line manager - complete the table below:
Day
Week 1
Week 2
Week 3
Week 4
Mon
856
805
831
814
Tues
932
947
968
945
Wed
218
899
910
963
Thur
945
932
203
977
Fri
456
475
453
421
Total for week
Rounded total
Now you need to work out the monthly figures. Remember to go back to your original
weekly totals first before you round your answer - can you think why?
Your line manager asks you to explain the differences in the daily production figures. How
might you answer him?
Weekly totals: 3407, 4058, 3365, 4120 Rounded weekly totals: 3410, 4060, 3370, 4120
Overall total: 3407 + 4058 + 3365 + 4120 = 14,950
Rounded monthly total: 15,000 (notice that this looks as if it’s been rounded to the nearest 1,000 but it’s the
knock-on effect from the 5)
Possible explanations for differences:
Mondays are lower – team meeting every Monday morning/machines need to warm up
Fridays are lower – half day working/machines need to be cleaned down
Wed week 1 and Thurs week 2 – machine broke down/machine needed service/waiting for raw materials
Beware of estimates or rounding
In certain circumstances it is not appropriate to estimate or round answers - here are a
few; think of others yourself:
• Your friend owes you £447 and offers to give you £400 (rounded to the nearest 100)
• The drug dose is 27mg so the doctor gives 30mg (rounded to the nearest 10)
• The machine part needs to be engineered to 0.75mm so the operator does it to 1mm
(rounded to the nearest whole number)