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A quick rounding question!

Discussion in 'Mathematics' started by misconception, Oct 1, 2015.

  1. misconception

    misconception New commenter

    If you were asked to round 9.95 to the nearest tenth, would the answer be 10, 10.0 or would either be correct?
  2. mon_ster

    mon_ster New commenter

    10.0 implies the degree of accuracy is 1 d.p or 3.s.f.
    Skillsheets and misconception like this.
  3. colinbillett

    colinbillett Occasional commenter

    10.0 or 9.9 are both mathematically correct, since the 5 is half way between these two. And when it comes to bounds, students need to know that 9.9 when given to the nearest tenth is between 9.85 and 9.95. So telling them to round up always when they see a five usually leads to problems when they come to bounds, because 'I've always been taught to...'. However, in exam questions on rounding, I don't think I've ever seen a case that could be given either up or down, probably because teachers don't understand, or maybe the examiners don't like a choice of answers.
  4. frustum

    frustum Star commenter

    Now what about 9.95 to 2s.f.?

    (Even more unlikely to come up in an exam, fortunately, and in real life I think a judgement call is permissible.)
  5. maths126

    maths126 New commenter

    Strictly speaking, Significant Figures are best dealt with using Standard Form.
    Thus 9.95 to 2 s.f. is 1.0 x 10^1
  6. JaquesJaquesLiverot

    JaquesJaquesLiverot Established commenter

    Presumably round up every number ending in 5 also leads to a set of numbers with a greater sum or mean?

    I seem to remember there being a rule when I was at school that numbers were rounded such that the final digit was always either odd or even (according to which convention you'd agreed), so that half of 5s get rounded up and half get rounded down to avoid errors. None of my colleagues remembers this, though.
  7. blueskiesmev

    blueskiesmev New commenter

    9.9 to the nearest tenth is less than 9.95 and equal to or greater than 9.85. 9.95 rounded to the nearest tenth would be 10.0.

    If I am one of the "teachers that don't understand" please explain it to me.

    My understanding is that when rounding we are considering the values from 0 - 9.999999999999.... therefore the mid-point is in the non-existent gap between 4.999999999999... and 5. Therefore anything below 5 is rounded down and 5 and above is rounded up.
  8. frustum

    frustum Star commenter

    JacquesJacques, I've come across that convention, although never in schools. The argument for it is that if 5 is always rounded up, and you're looking at totals across a very large number of items, there's a net drift upwards of the figures. With a rule that means half of the 5s are rounded each way, the overall total should reflect things more accurately.
  9. JaquesJaquesLiverot

    JaquesJaquesLiverot Established commenter

    Speaking of rounding, is anyone else perplexed by the number of stars awarded to resources?

    An average rating of 4.3 gets four stars, and a rating of 4.7 gets five stars. Apparently only an average of 4.5 would give you four-and-a-half stars. And would that even be possible if you had a (moderate) odd number of reviews?
  10. coyote

    coyote New commenter

    When deciding how to round, the digit you are considering is one of 0123456789
    10 possibilities. Round first 5 down, 2nd 5 up. so 5 is rounded up.
    Other things being equal of course...
  11. JaquesJaquesLiverot

    JaquesJaquesLiverot Established commenter

    You could equally argue that the 0 doesn't need changing, so there are only nine digits to consider.
  12. coyote

    coyote New commenter

    Well, no.
    If I round to n sig figs then the (n+1)th digit is the one under consideration, and used to determine whether or not the nth digit is to be changed (increased by 1). All digits after the nth are then removed.
  13. PaulDG

    PaulDG Occasional commenter

    What's prompted this question? Is it the new GCSE?

    My thoughts are "a tenth of what??"

    Does the question refer to the absolute error of "correct to 1 decimal place"?

    Or does it refer to a relative error - a potential error of +/- 0.995 ?

    I'm starting to see a lot of clumsy-worded so-called 'problem solving' questions that are causing more far problems than they solve ;)
  14. misconception

    misconception New commenter

    Ah - thanks Paul - your comment has prompted me to go back to the NC14 objective (year 5) that I am teaching and it actually says -
    'Round decimals with two decimal places to the nearest whole number and to one decimal place'.

    So my new question is...
    If you were asked to round 9.95 to one decimal place, would the answer be 10, 10.0 or would either be correct?
    I was prompted to ask this question as I remember a KS2 sats question a couple of years ago where there was a lot of discussion about the mark scheme for a rounding question but I cant actually find that mark scheme and so I thought I would post it here.

    Thanks everyone for taking the time to help.
  15. maths126

    maths126 New commenter

    The only correct answer is 10.0 since 10 on its own has no decimal places. The choices for children to consider are 9.9 and 10.0. They should learn that "5s round up" (for the reasons explained by Coyote above) and so they write down "9.95 is 10.0 to one d.p." as their answer.
  16. racroesus

    racroesus Star commenter

    It was a convention used by the OU.
  17. racroesus

    racroesus Star commenter

    The OU also used the convention of rounding up on the 5 for positive numbers and rounding down on negative numbers: 0.65 to 0.7 and -0.65 to -0.7.

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