How do you round decimal figures?

[cakedup]

So how would you round, to one one significant figure, 0.46 for example? Because we've tried 0.5, 0, and 1 and none of them seem to be right!

meanwhile DS has given up and gone on his phone

You need to round 23.4 and 13.9 to 1 sig fig too, which would be 20 x 10.

If you get a calculation that you can’t do in your head (e.g. 23x14) you’ve gone wrong.

sashh 1 significant figure, but I see your point which might help in further questions. Previously I just presumed rounding off to the nearest whole number.

Rounding to 1 sig fig means rounding to the number with the highest place value. So in 23.4 that’s rounding to the nearest 10. In 0.18 the nearest tenth, in 0.018 the nearest hundredth.

You're right noblegiraffe ! I just thought rounding to one significant figure literally meant up 1 or down 1

BODMAS

The division is done before the multiplication, that’s why your answer is wrong.

* 8.2 x 6.7 divided by 0.46*

Round 0.46 up to 0.5.

6.7/0.5= 13.4

8.2 x 13.4 = 109.88

To estimate I would do 8 x 13.5, answer 108 approx.

No, nothing to do with Bodmas at all. division and multiplication are the same order of priority (because they are the same thing, really) and it makes no difference which way round you do them.

It's all to do with what degree you round to, and when.

* So 23.4 x 13.9 divided by 0.18*

So wouldn't that be:
23 x 14 = 322
322 ÷ 0.2 = 1610

No this one is also wrong as you have not followed bodmas again.

14/0.2 = 70

23.5 x 70 = 1645

The actual answer is 1807 when exact figures used.

with significant figures, there should be only 1 number that isn't a 0 (if it's 1 sf) or 2 or whatever is asked for.

I don't like them much, because I'd always rather things are rounded to the same degree of accuracy, and if you have numbers that are close to a place value boundary, you get somewhat misleading results for your experiment or whatever.

* No, nothing to do with Bodmas at all. division and multiplication are the same order of priority (because they are the same thing, really)*

Since when? It’s brackets, orders, division, multiplication, addition, subtraction. When did the rules change to allow multiplication first?

division is done before the multiplication

No! Division and multiplication are done at the same time, or from left to right if necessary. Bodmas is misleading as it’s not strictly that order.

But these estimation questions are usually written as a fraction anyway so the multiplication is definitely done first as we treat the top and bottom of fractions as if they have brackets around them.

Well every day is a school day! I don’t understand maths anymore!

but for your help

Bodmas really is irrelevant here.

to 1 sig fig, you have 20 x 10 / 0.2

You can do 20/0.2 = 100
100 x 10 = 1000

Or

20x10 = 200
200/0.2 = 1000

Or 10/0.2 = 50
50x200 = 1000

It's all the same thing.
All that matters here is when and how much you choose to round things.

And even with that, there's not a 'right' and 'wrong', but what choices you make depending on how accurate you need your answer to be
(or, in this case, what an examiner has specified you should do in a question!).

FruitCider join my club!

the rules have never changed; it's just that people have often misunderstood them.

In other countries ,it might be learned as PEMDAS, with the M before the D (and P standing for parentheses and the E for exponents).

We only say Bodmas as it's a nicer, easier word than Bomdas, but that would be equally true.

You don't need to do Addition before Subtraction, either - they are also basically the same thing, as long as you keep the sign with the number that comes afterwards.

eg, 8 - 5 + 2

You can do -5 + 2 + 8
or 8 + 2 -5
or 2 - 5 + 8

or whatever you like - the important bit is that the sign stays with its number. It's easier to not really think of it as 'addition' or 'subtraction', either, but just collecting like terms , some that are positive and some that are negative.

If you followed BODMAS strictly, 4-5+2 would be 4 - 7 which is -3
However, the correct answer is 1. I tend to teach it in a triangle rather than a list
B
O (except I use I not O)
DM (left to right)
AS (left to right)

caked more importantly than BODMAS, do you get the estimation thing now?

Rather than estimate mean 'work out a rough answer to this calculation', in maths GCSE it means 'round everything to one sig fig then do the calculation in your head' and you will lose marks if you just 'reckon' an answer.

I don't even suggest that DM and AS have to be done left to right, as long as students understand about keeping the signs with the number.

I tell them they can do whatever makes the calculation easier.

If it's 18x8/2 , and then want to do 18/2 first to get 9x8, because they know their 9 times tables, then I tell them great - do that, and you won't have to deal with bigger numbers like 18x8 if you don't want.

Or if 7 / 2 x 8 is complicated because you get 3.5 and you don't like decimals, well ok, then do 7x8 and then divide that by 2, and you'll stay in the world of whole numbers.

etc.

Same with lots of + and - if you collect all the + together and all the - together, then only one calculation that involves them both together at the end, if that's the bit you don't like., etc

It does rely on students properly understanding how and when they can do this, though (i.e., all the terms multiplied or divided together; keeping signs with numbers before adding/subtracting, etc). But it can make some calculations easier.

does rely on students properly understanding how and when they can do this

Yes, which is why 'left to right' is helpful in giving them something that works instead of leaving them in a muddle when they can't remember how to manipulate the numbers themselves.

noblegiraffe yes I think I get it now. Sorry, I'm having to ignore the comments on BODMAS because my brain literally cannot handle anymore.

We've now completed DS' maths homework!

DS would like to say: "Thank you all of you. Thanks you've really helped me through my stress. I feel a bit more relaxed about going back to school."

Aww that's nice of your DS. What a polite boy! Hope he thanked you too!

Oh he did noblegiraffe , not great at maths but excellent at thanking!