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Maths year 11

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I got one for you. Express 0.1˙23456790˙ 0.\dot{1}2345679\dot{0} as the ratio of two integers.
Original post by Ano123
I got one for you. Express 0.1˙23456790˙ 0.\dot{1}2345679\dot{0} as the ratio of two integers.


123456789010101\frac{1234567890}{10^{10}-1}
(edited 7 years ago)
Original post by RDKGames
123456789010101\frac{1234567890}{10^{10}-1}

In the form a/b a/b where gcd(a,b)=1 \text{gcd}(a,b)=1 .
Original post by Ano123
In the form a/b a/b where gcd(a,b)=1 \text{gcd}(a,b)=1 .


Oh come on, that's not what we agreed on. :frown:
Original post by Ano123
In the form a/b a/b where gcd(a,b)=1 \text{gcd}(a,b)=1 .


1371742101111111111\frac{137174210}{1111111111}? Division by 9. Can't figure out any more common divisors.
Original post by RDKGames
1371742101111111111\frac{137174210}{1111111111}? Division by 9. Can't figure out any more common divisors.


The answer is 10/81 10/81 . It's easier to consider the expansion of x(1x)2 \frac{x}{(1-x)^2} . If you make x=0.1 x=0.1 it gives you want you want,
Reply 886


Why do we multiply it by 10x or 100x ?
Original post by z_o_e
Why do we multiply it by 10x or 100x ?


For the same reason why we would multiply 0.5 by 10 while in the process of finding a fraction for it. It makes it easy to find the fraction for it before simplifying it, and it turns the right side into a whole number which is important. We can apply the same idea with 0.5 but we do not need to take anything away because we wouldn't have any repeating decimals.

x=0.5x=0.5

10x=510x=5

x=510=12x=\frac{5}{10}=\frac{1}{2}

and the method you're familiar with is:

0.5=0.51=510=120.5=\frac{0.5}{1}=\frac{5}{10}= \frac{1}{2}

which has it's similarities if you ignore the xx
(edited 7 years ago)
Reply 888
Original post by RDKGames
For the same reason why we would multiply 0.5 by 10 while in the process of finding a fraction for it. It makes it easy to find the fraction for it before simplifying it, and it turns the right side into a whole number which is important. We can apply the same idea with 0.5 but we do not need to take anything away because we wouldn't have any repeating decimals.

x=0.5x=0.5

10x=510x=5

x=510=12x=\frac{5}{10}=\frac{1}{2}

and the method you're familiar with is:

0.5=0.51=510=120.5=\frac{0.5}{1}=\frac{5}{10}= \frac{1}{2}

which has it's similarities if you ignore the xx




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Reply 890
Original post by RDKGames
Not quite.


Explanation please

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Original post by z_o_e
Explanation please

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Because you're layout makes it confusing and nothing there adds up.

x=0.5˙8˙=0.5858...x=0.\dot5\dot8=0.5858...

10x=5.8585...10x=5.8585... (NOT 0.58 like you shown)

100x=58.5858...100x=58.5858...

try and work it from there. Think about which ones will make the decimals cancel via subtraction.
(edited 7 years ago)
Reply 892
Original post by RDKGames
Because you're layout makes it confusing and nothing there adds up.

x=0.5˙8˙=0.5858...x=0.\dot5\dot8=0.5858...

10x=5.8585...10x=5.8585... (NOT 0.58 like you shown)

100x=58.5858...100x=58.5858...

try and work it from there. Think about which ones will make the decimals cancel via subtraction.




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Reply 894
Original post by RDKGames
That's better.




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Reply 896
Original post by RDKGames
Yes


How would I do this?

Question D
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Original post by z_o_e
How would I do this?

Question D
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Well think about it and tell me. Also, you wrote down your x wrong.

0.2˙45˙0.\dot24\dot5 means 0.245245245... where the 245's are the one's repeating; i.e. everything in the gap between the two dots.
Reply 898
Original post by RDKGames
Well think about it and tell me. Also, you wrote down your x wrong.

0.2˙45˙0.\dot24\dot5 means 0.245245245... where the 245's are the one's repeating; i.e. everything in the gap between the two dots.




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Perfect. I think you got the hang of this now, and I doubt GCSE would often ask you to turn repeating decimals into fractions. :h:

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