Quick maths question

cowasaki

cowasaki

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Youngest lad has a maths homework question

find the fraction: 0.372727272 recurring.

now I am a bit of a maths head and have never been stumped by a homework question before but this is a non calculator question!!

I could not for the life of me work out how to get the answer easily !!

Now what I did was to write a quick javascript routine:

Code: 
constant=0.372727272727272727272;

out="";

for (var i = 1; i < 500; i++) { 
 out=out+"\r"+i+"  "+i*constant;
};

alert(out);

which goes through all the numbers from 1 to 500 and means that I could find that the actual answer is 41/110.


Now does anyone know how a 14 year old is supposed to get this answer ??
 
cowasaki said:
Now does anyone know how a 14 year old is supposed to get this answer ??
Click to expand...

off the internet.....like the rest of their homework :lol:

Seriously though, wouldn't it just be rounded up to 0.38, which is 19/50 as a fraction :shrug:
 
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Must admit I was stumped too - could it have been written down wrong and was meant to be 0.2727272727 as that would just involve multiplying by 99 to give 27/99, or 3/11?

A single repeating digit = multiply by 9
two repeating digits = multiply by 99
three digits = 999 etc

Seems very difficult for a 14 year old - I remember something to do with repeating digits being on GCSE, but that never had anything where there was a non-repeating digit followed by a repeate sequence
 
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No it was written down correctly, it was out of a book :)

Stumped me too as the way that was pointed out is the way I told him to do it !!! But then he came back saying he couldn't find an answer so I had a closer look. I still couldn't find an answer that looked like a 14 year old would have managed the maths so I spent 2 minutes to find the answer using the javascript program in order to try and reverse engineer the method but even with the answer it still looked rather odd !!!

Oh well this is rather strange, I wonder what his teacher will say. He is at the top of set 1 so the teacher may just have chucked them a wide ball just to see if anyone manages it :)

At least someone hasn't come back and said "you do it like this you plonker" :bat:
 
Well I have checked out the BBC bitesize web site and their method is basically the same as the method I gave him but it is the a little more complicated that the bitesize website allows for. I will find out later when he gets home but I think it was the teacher giving them one question that was a lot harder to find out if anyone could manage it :)
 
So glad I dont have to do maths anymore :D
Thats insanely hard!!
 
Worked it out on paper once I had free time. You need to remove the first part, then multiply out by 99 (repetition based around two digits)

its 3/10 + (72/99)*1/10 (the 0.1 is to take account of the 0.3 treated seperately)..... which multiplies out to 297/990 + 72/990, or 369/990 and then divide by 9 to get 41/110
 
Uneducated_Rick said:
Worked it out on paper once I had free time. You need to remove the first part, then multiply out by 99 (repetition based around two digits)

its 3/10 + (72/99)*1/10 (the 0.1 is to take account of the 0.3 treated seperately)..... which multiplies out to 297/990 + 72/990, or 369/990 and then divide by 9 to get 41/110
Click to expand...

Excellent that's really good. I have shown him and he now understands it. My method using javascript looks just as easy :) This is one of those things that has been added to the curriculum since I did 'O' level and 'A' level maths to replace something else. I can't believe they don't have to put up with calculus anymore :)
 
Yes but the little darlings couldn't do it which upset the pass mark!

The school's method was this:

0.37272=x

372.72=1000x
3.72=10x
369=990x

369/990 = x

x = 41/110

I tried to explain that this was basically the same method !!
 
cowasaki said:
Yes but the little darlings couldn't do it which upset the pass mark!

The school's method was this:

0.37272=x

372.72=1000x
3.72=10x
369=990x

369/990 = x

x = 41/110

I tried to explain that this was basically the same method !!
Click to expand...

How do you make the logical step down from 369/990=x to find out the smallest fraction of 41/110=x.

:thinking::bang:

Edit- this was never covered at school, and I was hopeless at calculus as well
 
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singlespeed said:
How do you make the logical step down from 369/990=x to find out the smallest fraction of 41/110=x.

:thinking::bang:

Edit- this was never covered at school, and I was hopeless at calculus as well
Click to expand...

369/990 simplified to 41/110 ---- divide by 9

>>> I like calculus :)
 
Even with the answer posted I'm lost
 
cowasaki said:
Yes but the little darlings couldn't do it which upset the pass mark!

The school's method was this:

0.37272=x

372.72=1000x
3.72=10x
369=990x

369/990 = x

x = 41/110

I tried to explain that this was basically the same method !!
Click to expand...

Why the 372.72=1000x step ?

why not go straight to 3.7272=10x ?
*99 is 368.99 = 990x
divided by 9 is 41/110
 
I completely understand it, it is just that I had never seen this type of question before. The contents of the GCSE maths syllabus has changed from the 'O' level one so there are a few things I have never come across before (although most of them are easy enough to work out). The explanation pointed to earlier (I think by Outlore) on BBC's bitesize was the best explanation. The school's explanation was basically the same thing by a different method. My method involved a for next loop and a few lines of javascript so it would be ruled out in a non calculator exam !! My alternative method involved trial and error which again was not really ideal as it would have taken longer but I know how to do it now so it doesn't matter ;)

It going to be fun when he starts 'A' level maths though, its a long time since I did that and having not used any of it since I will have forgotten most of it. He will overtake me then and I can ask him :)
 
EdBray said:
Why the 372.72=1000x step ?

why not go straight to 3.7272=10x ?
*99 is 368.99 = 990x
divided by 9 is 41/110
Click to expand...

I think it was an attempt at making the maths easier for the kids by the teacher (ie 1000x-10x = 990x).
 
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