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I'm in year 10 and have a B grade - yet still manage to mess it up when I face a question regarding decimals. For example: Round 8.647 to one decimal place. Would this be 8.7 or 8.6 as I have never understood if the third number affects the second number first.

Also recurring decimals, say for example: Round 8.56565656 to two decimal places Would this be 8.67 and the first and second are rounded, or 8.57, or 8.56? Finally, Would 8.045 = 8.05? or 8.15?

Harry Kitchener
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  • Maybe just as a trick, you might multiply 8.647 by ten and then round to the nearest whole number. Is it any easier to see that 86.47 rounds to 86? – Jason Zimba Apr 01 '14 at 19:42
  • The thing is that you need to know if you are closer to $8.6$ or to $8.7$. And if you are in the middle, you go up (by convention). – Jérémy Blanc Apr 01 '14 at 20:01
  • It can help to visualize the numbers on the number line. Kind of like this for example. – littleO Apr 01 '14 at 20:26
  • @JérémyBlanc There are many different conventions for what to do when rounding from an exact midpoint value - I would say that the most 'common', particularly in computer sciences, is to round so as to make the last digit even - so 8.645 would round to 8.64, while 8.655 would round to 8.66. – Steven Stadnicki Apr 02 '14 at 06:11
  • OK, I did not know this strange convention, but thanks for explaining it. I would say that in maths, this is the other one that we use. – Jérémy Blanc Apr 02 '14 at 07:16

2 Answers2

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To round to either $8.6$ or $8.7$, compare them with the middle value of both which is $8.65$. The question is do you have :$$8.647 < 8.65\qquad \text{ or } \qquad 8.647 \ge 8.65$$

In the first case you round down to $8.6$, in the second case you round up to $8.7$.

Same goes with $8.565656$, take the middle value of $8.56$ and $8.57$, which do you have :$$8.565656 < 8.565\qquad \text{ or } \qquad 8.565656 \ge 8.565$$

If your problem is comparing decimals, I suggest you have a look at this Khan Academy video which explains it well.

user88595
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Suppose you want a number correct to $i$ decimal places. Just look at the $i+1$ th digit. If its a $5$ or greater, round up. If its a $4$ or lower, round down.

  • Round down = forget everything after the $i$th digit

  • Round up = forget everything after the $i$th digit, and increment the $i$th digit by $1$.

For example, if you want $8.647$ correct to $1$ decimal place, you need to be looking at the digit immediately after the $6$. In this case its $4$. So you round down. Final answer: $8.6$

goblin GONE
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  • The only argument with this is what to do with exactly $5$. There are various standards. You are always rounding up, which is one standard. – Ross Millikan Apr 01 '14 at 19:55
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    @RossMillikan true; im just repeating the convention we were taught in high school. – goblin GONE Apr 01 '14 at 20:37
  • Brilliant answer, however how would I round the recurring decimal? – Harry Kitchener Apr 01 '14 at 20:38
  • @HarryKitchener, the only trick with recurring decimals is that if there's an infinite tail of $9$'s (as in 4.1399999...) you first have to eliminate the tail. Replace the $9$'s with $0$'s and increment the number immediately to the left of the tail. e.g. in this case we increment $3$. So we get $4.14$ (which is equal to the number we started with, just written more simply). Now you can apply the usual rules. Hence if you want $8.56565656...$ to two decimal places, just apply the rules given in my answer (since there is no recurring tail of 9's). – goblin GONE Apr 02 '14 at 05:33
  • So basically, look at it like $(8.56)(5)(65656...).$ Notice that we've got a $5$ in those lonely brackets. So we round up. Final answer; $8.57$. – goblin GONE Apr 02 '14 at 05:35
  • @HarryKitchener please comment if that's unclear. – goblin GONE Apr 02 '14 at 05:36