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GCSE Maths help: Upper bounds and lower bounds

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1. Hi, I was wondering how to work out the upper and lower bound of numbers rounded to the nearest ____

with ___ being: 1 decimal, 2 decimal, different no. of significant figures, nearest 10s, 100s, and any other rounding types you can think of that may appear on GCSE maths exams.
(For example a question might say:
Katie ran 5682 km rounded to the nearest ___ (km in this case but could be decimal place, sig. fig. and many other types). Work out the upper and lower bound of this.

Can someone please post a number and show me what the upper bound and lower bound is to it in the forms (e.g. 3 sig. fig) and also explain to me how I would do it with any other number.

I can kinda do rounded to nearest 1 or 2 decimal place but some are hard just as hundreth of a second or some sig figs AND ANY OTHER types of ways numbers may be rounded in..

I can do: Find the upper bound of 6.8 rounded to 1 decimal place. = 6.85
just the harder ones which don't ask for decimal places are a bit tricky...

By the way, this is for the calculator GCSE paper.

Thank you
2. (Original post by Princestia)
Hi, I was wondering how to work out the upper and lower bound of numbers rounded to the nearest ____

with ___ being: 1 decimal, 2 decimal, different no. of significant figures, nearest 10s, 100s, and any other rounding types you can think of that may appear on GCSE maths exams.
(For example a question might say:
Katie ran 5682 km rounded to the nearest ___ (km in this case but could be decimal place, sig. fig. and many other types). Work out the upper and lower bound of this.

Can someone please post a number and show me what the upper bound and lower bound is to it in the forms (e.g. 3 sig. fig) and also explain to me how I would do it with any other number.

I can kinda do rounded to nearest 1 or 2 decimal place but some are hard just as hundreth of a second or some sig figs AND ANY OTHER types of ways numbers may be rounded in..

I can do: Find the upper bound of 6.8 rounded to 1 decimal place. = 6.85
just the harder ones which don't ask for decimal places are a bit tricky...

By the way, this is for the calculator GCSE paper.

Thank you
add 0.5 for upper bound and minus 0.5 for lower bound. post a question next time not an essay. thanks, its too much to read.
3. (Original post by 130ss)
add 0.5 for upper bound and minus 0.5 for lower bound. post a question next time not an essay. thanks, its too much to read.
Yeah adding/minus 0.5 only works for certain types e.g. rounded to 1 decimal place doesn't it? It doesn't work for all cases.. I think..
Lol sorry.. I can never be concise and I just wanted to be clear so I people won't be saying: "huh? What??" or replying about something that I don't mean lol...
thanks anyway though
4. (Original post by Princestia)
Yeah adding/minus 0.5 only works for certain types e.g. rounded to 1 decimal place doesn't it? It doesn't work for all cases.. I think..
Lol sorry.. I can never be concise and I just wanted to be clear so I people won't be saying: "huh? What??" or replying about something that I don't mean lol...
thanks anyway though
add or minus .5 after the decimal. if the question is upper bound of 8 = 8.5
upper bound of 8.4 =8.45
its hard to explain
5. (Original post by 130ss)
add or minus .5 after the decimal. if the question is upper bound of 8 = 8.5
upper bound of 8.4 =8.45
its hard to explain
lol thanks.. yeah i do get what you mean.. but I mean what if it's a number that doesn't contain a decimal point and the question says it's rounded to the nearest hundredth or something like that? I'm sure the answer would not be to 0.5 for the upper bound and minus 0.5 for the lower bound..
Thanks for posting again though
6. (Original post by Princestia)
lol thanks.. yeah i do get what you mean.. but I mean what if it's a number that doesn't contain a decimal point and the question says it's rounded to the nearest hundredth or something like that? I'm sure the answer would not be to 0.5 for the upper bound and minus 0.5 for the lower bound..
Thanks for posting again though
I understand what you're saying. Basically if its nearest hundreth, go to the thousands and +-5 thousandths. Its easier to explain with numbers then words is think.

So

0.5 = 0.45 - 0.55
0.65 = 0.645 - 0.655
0.7663 = 0.76625 - 0.76635

So you're basically going one extra place and adding +- 5 of that, hopefully you get what I mean.

Sometimes you might get for example

630 is accurate to the nearest 10, what is the upper and lower bound?

As its nearest 10, go to hundreds and do +- 5, so that would be 625 - 635.

Hopefully that's clear, someone else will probably be able to explain it better.
7. (Original post by Princestia)
lol thanks.. yeah i do get what you mean.. but I mean what if it's a number that doesn't contain a decimal point and the question says it's rounded to the nearest hundredth or something like that? I'm sure the answer would not be to 0.5 for the upper bound and minus 0.5 for the lower bound..
Thanks for posting again though
image a number with no decimal, jut imagine that at the end of a number it has a decimal. so 145 = 145. or 174395 = 174395.
then just use this rule.
8. 10.52-
Is the lower bound 10.515 and the upper bound 10.525?
9. (Original post by the don)
10.52-
Is the lower bound 10.515 and the upper bound 10.525?
yes
10. (Original post by Princestia)
Hi, I was wondering how to work out the upper and lower bound of numbers rounded to the nearest ____

with ___ being: 1 decimal, 2 decimal, different no. of significant figures, nearest 10s, 100s, and any other rounding types you can think of that may appear on GCSE maths exams.
(For example a question might say:
Katie ran 5682 km rounded to the nearest ___ (km in this case but could be decimal place, sig. fig. and many other types). Work out the upper and lower bound of this.

Can someone please post a number and show me what the upper bound and lower bound is to it in the forms (e.g. 3 sig. fig) and also explain to me how I would do it with any other number.

I can kinda do rounded to nearest 1 or 2 decimal place but some are hard just as hundreth of a second or some sig figs AND ANY OTHER types of ways numbers may be rounded in..

I can do: Find the upper bound of 6.8 rounded to 1 decimal place. = 6.85
just the harder ones which don't ask for decimal places are a bit tricky...

By the way, this is for the calculator GCSE paper.

Thank you
Examples of lower and upper bounds:

15 to the nearest 5.
UB = 17.5
LB = 12.5

320 to 2 sig fig.
UB = 325
LB = 315

2.34 to 2 decimal places.
UB = 2.345
LB = 2.335

You just need to know how to find the lower and upper bounds of numbers and then use that to answer questions.
11. What is 124 upper and lower bound then???
12. Easiest way I can think of explaining it is to do the following:
If it's to 1dp, then 0.1 / 2 = 0.05, so add 0.05 for UB and minus 0.05 for LB.
If it's to 2dp then 0.01 / 2 = 0.005, so add 0.005 for UB and minus 0.005 for LB
If it's to the nearest whole number, then 1 / 2 = 0.5, so add 0.5 for UB and minus 0.5 for LB
If it's to the nearest 5, then 5 / 2 = 2.5, so add 2.5 for UB and minus 2.5 for LB
If it's to the nearest 10, the 10 / 2 = 5, so add 5 for UB and minus 5 for LB
If you are given SF, see what column the SF you have rounded to are in and do the same to that columns value, e.g.234000 rounded to 3sf. The 3rd SF is located in the Thousands column so, 1000 / 2 = 500, so add 500 to give UB and minus 500 to give LB
UB = 234500 and LB = 233500
Use this method and you can't go wrong!
13. Does anyone know the topics that may come up for GCSE higher calculator aqa for this summer

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