How can i find 0.13r(as in the 3 recurring) as a fraction

  • Thread starter harlatt
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    Fraction
In summary, to find 0.13r as a fraction, you can use the shortcut of splitting it into 0.1 and 0.033333 and then adding the fractions together. This can be done by thinking of 0.033333 as 1/30 and 0.1 as 1/10, which simplifies to 4/30. Finding a common factor between 4 and 30, we get 2, and simplifying 4/30 gives us 2/15.
  • #1
harlatt
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How can I find 0.13r(as in the 3 recurring) as a fraction

Can anyone give me an idea of how I can find 0.13 as a fraction?
:uhh:
 
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  • #2
think of 0.133r as 0.1 + 0.033333r... and then add the fractions together.
 
  • #3
Hi there harlatt and welcome to PF,

From wikipedia:
Wikipedia said:
A shortcut in converting a repeating decimal to a fraction

If the repeating decimal is between 0.1 and 1, and the repeating block is n digits long occurring right at the decimal point, then the fraction (not necessarily reduced) will be the n-digit block over n digits of 9. For example,

* 0.444444... = 4/9 since the repeating block is 4 (a 1-digit block),
* 0.565656... = 56/99 since the repeating block is 56 (a 2-digit block),
* 0.789789... = 789/999 since the repeating block is 789 (a 3-digit block), etc.

If the repeating decimal is between 0 and 0.1, and the repeating n-digit block is preceded only by k digits of 0 (all of which are to the right of the decimal point), then the fraction (not necessarily reduced) will be the n-digit block over the integer consists of n digits of 9 followed by k digits of 0. For example,

* 0.000444... = 4/9000 since the repeating block is 4 and this block is preceded by 3 zeros,
* 0.005656... = 56/9900 since the repeating block is 56 and it is preceded by 2 zeros,
* 0.0789789... = 789/9990 since the repeating block is 789 and it is preceded by 1 zero.

For any repeating decimal not perscribed above, it can be written as a sum of a terminating decimal and a repeating decimal of one of the two above types. For example,

* 1.23444... = 1.23 + 0.00444... = 123/100 + 4/900 = 1107/900 + 4/900 = 1111/900
* 0.3789789 ... = 0.3 + 0.0789789... = 3/10 + 789/9990 = 2997/9990 + 789/9990 = 3786/9990 = 631/1665

The whole document can be found here: http://en.wikipedia.org/wiki/Recurring_decimal

Hope this helps:smile:
 
  • #4
:eek: :eek: :eek: :eek: :eek:

Sorry but i rlly don't get none of it lol
 
  • #5
ohhhhhh i get it! cheers thanks sooo much!
 
  • #6
wud it be 3/19 or is tht completely rong
 
  • #7
its not 3/19, but what was your work that got you there, maybe we can point out an error.
 
  • #8
harlatt said:
wud it be 3/19 or is tht completely rong
Nope, not quite.
 
  • #9
erm...

to be honest i don't get it now :(

im gettin rlly stressed cos I've been on this question for bout an hour nd have no clue
 
  • #10
so the numbe .1333 can easily be divided into 0.1 and 0.033333
.1 is easy as 1/10
but using hootenannny's post what would 0.03333333333 in fraction form?
 
  • #11
is it 15/90?
 
  • #12
harlatt said:
erm...

to be honest i don't get it now :(

im gettin rlly stressed cos I've been on this question for bout an hour nd have no clue
Okay, so we have the decimal [itex]0.1\dot{3}[/itex]; this can be split into two decimals thus;

[tex]0.1\dot{3} = 0.1 + 0.0\dot{3}[/tex]

Now, can you write [itex]0.1[/itex] and [itex]0.0\dot{3}[/itex] as fractions?
 
  • #13
harlatt said:
is it 15/90?
No, but very very close.
 
  • #14
is the whole answer 15/90 I've gone thru what the wikipedia thing has?
 
  • #15
erm..... illl try agen one sec
 
  • #16
The answer is not 15/90. Try doing what was suggested above and show your work
Hootenanny said:
Now, can you write [itex]0.1[/itex] and [itex]0.0\dot{3}[/itex] as fractions?
 
  • #17
nope I am still gettin 15/90

i went

0.133333...= 0.1 + 0.033333
=1/10 + 3/90 = 12/90 + 3/90 = 15/90


where am i goin rong?
 
  • #18
No, try thinking of what 0.333... is as a fraction, then work out the relationship between that and 0.0333...
 
  • #19
i don't rlly no
 
  • #20
You're nearly there, you just need to add the fractions 1/10 and 3/90 together properly, 1/10 shouldn't become 12/90.
 
  • #21
:frown: :frown: :frown:

rlly don't get that, got to go bed now,

shud have come on earlier :(
 
  • #22
harlatt said:
i don't rlly no
Are you saying that you don't know what [itex]0.\dot{3}[/itex] is as a fraction?
 
  • #23
yh but i was plusin the 2 factions i.e 10 goes into 90 9 times so i times tht by the one nd add it to the 3
 
  • #24
0.3 as a fraction = 3/10 aint it?
 
  • #25
comon I've got to go bed :(
 
  • #26
:( gtg sorri ill wait for one more reply but anymore ill get shouted at
 
  • #27
I meant what is 0.33333333... as a fraction, note the dot above the 3 to denote the recurrence.
 
  • #28
Is it 3/9?
 
  • #29
harlatt said:
Is it 3/9?
Yes, which simplifies to 1/3. But you don't want 0.33333, you want 0.0333333; so what is 0.033333 as a fraction?
 
  • #30
is it 1/30?
 
  • #31
harlatt said:
is it 1/30?
Spot on. Now, RE one of my previous posts
Hootenanny said:
[tex]0.1\dot{3} = 0.1 + 0.0\dot{3}[/tex]
So, we now know that 0.1 = 1/20 and 0.03333 = 1/30, thus;

[tex]0.1\dot{3} = 0.1 + 0.0\dot{3} = \frac{1}{10} + \frac{1}{30} = ?[/tex]

Can you go from here?
 
  • #32
quick I am being shotued at now :( sorri to be a pain
 
  • #33
is it 4/30?
 
  • #34
no i think is 3/30
 
  • #35
harlatt said:
is it 4/30?
Yes, which simplifies to...
 
<h2>1. How do I convert a recurring decimal into a fraction?</h2><p>To convert a recurring decimal into a fraction, you can use the formula: <br> 0.13r = 0.13 + 0.0013 + 0.000013 + ... <br> This can be simplified to: <br> 0.13r = 13/100 + 13/10000 + 13/1000000 + ... <br> Using the formula for an infinite geometric series, we can solve for the fraction as: <br> 0.13r = 13/100 * (1/(1-1/100)) = 13/99 <br> Therefore, 0.13r can be written as a fraction of 13/99.</p><h2>2. Can all recurring decimals be written as fractions?</h2><p>Yes, all recurring decimals can be written as fractions. This is because a recurring decimal is a decimal that has a repeating pattern, which can be expressed as a fraction using the method mentioned in the previous answer.</p><h2>3. How can I tell if a decimal is recurring or terminating?</h2><p>A terminating decimal is a decimal that has a finite number of digits after the decimal point, while a recurring decimal has a repeating pattern of digits after the decimal point. To determine if a decimal is recurring or terminating, you can check if the digits after the decimal point repeat or not.</p><h2>4. Is there a shortcut for converting recurring decimals to fractions?</h2><p>Yes, there is a shortcut for converting recurring decimals to fractions, known as the "bar notation" method. This involves placing a bar over the repeating digits in the decimal and writing it as a fraction. For example, 0.13r can be written as 0.13<span style="text-decoration: overline">3</span> and converted to a fraction as 13/99.</p><h2>5. Can I use the same method to convert any recurring decimal into a fraction?</h2><p>Yes, the method mentioned in the first answer can be used to convert any recurring decimal into a fraction. However, it may not always result in a simplified fraction. In such cases, you can use the "bar notation" method to simplify the fraction further.</p>

1. How do I convert a recurring decimal into a fraction?

To convert a recurring decimal into a fraction, you can use the formula:
0.13r = 0.13 + 0.0013 + 0.000013 + ...
This can be simplified to:
0.13r = 13/100 + 13/10000 + 13/1000000 + ...
Using the formula for an infinite geometric series, we can solve for the fraction as:
0.13r = 13/100 * (1/(1-1/100)) = 13/99
Therefore, 0.13r can be written as a fraction of 13/99.

2. Can all recurring decimals be written as fractions?

Yes, all recurring decimals can be written as fractions. This is because a recurring decimal is a decimal that has a repeating pattern, which can be expressed as a fraction using the method mentioned in the previous answer.

3. How can I tell if a decimal is recurring or terminating?

A terminating decimal is a decimal that has a finite number of digits after the decimal point, while a recurring decimal has a repeating pattern of digits after the decimal point. To determine if a decimal is recurring or terminating, you can check if the digits after the decimal point repeat or not.

4. Is there a shortcut for converting recurring decimals to fractions?

Yes, there is a shortcut for converting recurring decimals to fractions, known as the "bar notation" method. This involves placing a bar over the repeating digits in the decimal and writing it as a fraction. For example, 0.13r can be written as 0.133 and converted to a fraction as 13/99.

5. Can I use the same method to convert any recurring decimal into a fraction?

Yes, the method mentioned in the first answer can be used to convert any recurring decimal into a fraction. However, it may not always result in a simplified fraction. In such cases, you can use the "bar notation" method to simplify the fraction further.

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