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Recurring decimal help

Reply 1


What's your question?
Reply 2
Original post by Zacken
What's your question?


I cant seem to solve it


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Reply 3
Sorry didnt realise that was upside down ImageUploadedByStudent Room1482332507.621981.jpg


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Reply 4
Original post by Zacken
What's your question?


Ive solved it!!
ImageUploadedByStudent Room1482332739.221107.jpg


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Reply 5
Anyone know how to solve these
ImageUploadedByStudent Room1482332862.467441.jpg


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Reply 6
Original post by z_o_e
Anyone know how to solve these
ImageUploadedByStudent Room1482332862.467441.jpg


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EDIT : Do not use this method in GCSE.

Using a similar method to what you've done previously:

0.52˙8˙=510+0.2˙8˙10\displaystyle 0.5\dot{2}\dot{8} = \frac{5}{10} + \frac{0.\dot{2}\dot{8}}{10}

Can you carry on from here?
(edited 7 years ago)
Reply 7
Original post by z_o_e
Sorry didnt realise that was upside down ImageUploadedByStudent Room1482332507.621981.jpg


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For these questions, do you just know that when you have two recurring digits then you have a fraction over 99 or do you have other working that I can't see? Is this the way your teacher has shown you?

I ask this because for example I am looking at a GCSE question that asks:

Prove that the recurring decimal 0.3˙6˙=4110.\dot{3}\dot{6}=\frac{4}{11}

If you were doing this, would you just say 0.3˙6˙=3699=4110.\dot{3}\dot{6}= \frac{36}{99} = \frac{4}{11} ?

Because that would get you 0/3 marks.

The way you're doing these questions is a bit unusual but maybe this is just an introductory method that your teacher has given you?
Reply 8
Original post by notnek
For these questions, do you just know that when you have two recurring digits then you have a fraction over 99 or do you have other working that I can't see? Is this the way your teacher has shown you?

I ask this because for example I am looking at a GCSE question that asks:

Prove that the recurring decimal 0.3˙6˙=4110.\dot{3}\dot{6}=\frac{4}{11}

If you were doing this, would you just say 0.3˙6˙=3699=4110.\dot{3}\dot{6}= \frac{36}{99} = \frac{4}{11} ?

Because that would get you 0/3 marks.

The way you're doing these questions is a bit unusual but maybe this is just an introductory method that your teacher has given you?


I watched this video and learnt this method.
https://youtu.be/FThDfpFLT7A



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Reply 9
Original post by z_o_e
I watched this video and learnt this method.
https://youtu.be/FThDfpFLT7A



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Wow okay so he has said that 0.7˙=79 0.\dot{7}=\frac{7}{9} \ because it is. He offers no explanation/proof.

For a recurring decimals proof question, you would get no marks unless you proved that the decimal is equal to a fraction without making assumptions.

I recommend you look at a GCSE textbook to see how you should be doing these questions. Have a go and if you're unsure of the method, feel free to ask us.

It looks like a lot of GCSE students are using this method judging by the comments because it's easier than what their teacher has shown them. I should probably send a message to the guy who makes the vid (I hope he's not a teacher).
How I learned this at GCSE was to multiply by factors of 10.

Example 1
What is the fraction equivalent to 0.7˙98˙0.\dot{7}9\dot{8}?
Step 1- Multiply until you get the same recurring decimal part.
In this case, we need to multiply by 100:
x = 0.798798...
1000x = 798.798798...
See how the decimal part is the same, but the whole number is different?
(This is why I chose 1000- if I chose 10, the decimal part would be different, e.g. 7.897897... This means we can't subtract easily to get rid of the recurring bit)
Step 2- Subtract
999x = 798
Step 3- Divide
x = 798/999 = 266/333 Final Answer

Example 2
What is the decimal equivalent to 0.91919191...
x = 0.919191...
100x = 91.919191...
99x = 91
x = 91/99 Final Answer

Example 3
What is the decimal equivalent to 0.123454545...
x = 0.123454545...
100x = 12.34545...
(Do not worry about the extra non-recurring parts, just make sure the recurring parts line up)
99x = 12.222 (no recurring)
x = 12.222/99 = 12222/99000 = 679/5500 Final Answer

This is more consistent method that works for any recurring decimal.
(edited 7 years ago)
Reply 11
Original post by Myleopard
How I learned this at GCSE was to multiply by factors of 10.

Example 1
What is the fraction equivalent to 0.7˙98˙0.\dot{7}9\dot{8}?
Step 1- Multiply until you get the same recurring decimal part.
In this case, we need to multiply by 100:
x = 0.798798...
1000x = 798.798798...
See how the decimal part is the same, but the whole number is different?
(This is why I chose 1000- if I chose 10, the decimal part would be different, e.g. 7.897897... This means we can't subtract easily to get rid of the recurring bit)
Step 2- Subtract
999x = 798
Step 3- Divide
x = 798/999 = 266/333 Final Answer

Example 2
What is the decimal equivalent to 0.91919191...
x = 0.919191...
100x = 91.919191...
99x = 91
x = 91/99 Final Answer

Example 3
What is the decimal equivalent to 0.123454545...
x = 0.123454545...
100x = 12.34545...
(Do not worry about the extra non-recurring parts, just make sure the recurring parts line up)
99x = 12.222 (no recurring)
x = 12.222/99 = 12222/99000 = 679/5500 Final Answer

This is more consistent method that works for any recurring decimal.


Thank you so much for this!!!

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