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

[harlatt]

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:

 

[dmoravec]

think of 0.133r as 0.1 + 0.033333r... and then add the fractions together.

 

[Hootenanny]

Hi there harlatt and welcome to PF,

From wikipedia:

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

 

[harlatt]

Sorry but i rlly don't get none of it lol

 

[harlatt]

ohhhhhh i get it! cheers thanks sooo much!

 

[harlatt]

wud it be 3/19 or is tht completely rong

 

[dmoravec]

its not 3/19, but what was your work that got you there, maybe we can point out an error.

 

[Hootenanny]

wud it be 3/19 or is tht completely rong

Nope, not quite.

 

[harlatt]

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

 

[dmoravec]

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?

 

[harlatt]

is it 15/90?

 

[Hootenanny]

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 $0.1\dot{3}$; this can be split into two decimals thus;

$$0.1\dot{3} = 0.1 + 0.0\dot{3}$$

Now, can you write $0.1$ and $0.0\dot{3}$ as fractions?

 

[Hootenanny]

is it 15/90?

No, but very very close.

 

[harlatt]

is the whole answer 15/90 I've gone thru what the wikipedia thing has?

 

[harlatt]

erm..... illl try agen one sec

 

[Hootenanny]

The answer is not 15/90. Try doing what was suggested above and show your work

Now, can you write $0.1$ and $0.0\dot{3}$ as fractions?

 

[harlatt]

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?

 

[Tomsk]

No, try thinking of what 0.333... is as a fraction, then work out the relationship between that and 0.0333...

 

[harlatt]

i don't rlly no

 

[Tomsk]

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.

 

[harlatt]

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

shud have come on earlier :(

 

[Hootenanny]

i don't rlly no

Are you saying that you don't know what $0.\dot{3}$ is as a fraction?

 

[harlatt]

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

 

[harlatt]

0.3 as a fraction = 3/10 aint it?

 

[harlatt]

comon I've got to go bed :(

 

[harlatt]

:( gtg sorri ill wait for one more reply but anymore ill get shouted at

 

[Hootenanny]

I meant what is 0.33333333... as a fraction, note the dot above the 3 to denote the recurrence.

 

[harlatt]

Is it 3/9?

 

[Hootenanny]

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?

 

[harlatt]

is it 1/30?

 

[Hootenanny]

is it 1/30?

Spot on. Now, RE one of my previous posts

$$0.1\dot{3} = 0.1 + 0.0\dot{3}$$

So, we now know that 0.1 = 1/20 and 0.03333 = 1/30, thus;

$$0.1\dot{3} = 0.1 + 0.0\dot{3} = \frac{1}{10} + \frac{1}{30} = ?$$

Can you go from here?

 

[harlatt]

quick I am being shotued at now :( sorri to be a pain

 

[harlatt]

is it 4/30?

 

[harlatt]

no i think is 3/30

 

[Hootenanny]

is it 4/30?

Yes, which simplifies to...