## Thursday, February 21, 2008

### Recurring decimal numbers are rational numbers

You can click on the link to find out how you can convert a recurring decimal number to a rational number.

http://mathforum.org/library/drmath/sets/select/dm_repeat_decimal.html

Share with me :-
1) an example of a recurring decimal and explain how you can convert it into a fraction.
(Please Do Not use the same examples given by others in the comments before yours!)

2) 20.0103030303....... as a fraction.

Think! Think! Think!

milton said...

when you divide a number and the answer has a whole long stretch of decimals(20.103030303),it can either be an imaginary number or real number.in this case there is recurring numbers (303) thus it can be expressed as a fraction.for example (0.3333333...)= 1/3

Barney Chan said...

it is a decimal that repeat its number
a recurring decimal number eg.
. .
0.12312312312312 is actually 123/999

Yihng said...

1) 0.3333333...=1/3

2) 20.010303030...=x
=100x=0.010303030...-x
=2001.03030303.....-x
=1981.02x100
=198102/9900-ans

Yihng said...

Teacher i was doing my answer when milton finished i never seehis 0.333333 so this is my new number

For example an recurring number
(0.333333),this is recurring numbers so it can be expressed as a fraction.for example (0.6666666...)= 2/3

ryansiow said...

When you divide a number and the answer has a whole long stretch of decimals.(0.123123123)it can either be an rational number or irrational number.in this case there is recurring numbers (123)thus it can be expressed as a fraction.For example(0.99999999999)=9/10

Foo Xiang Bing said...
Foo Xiang Bing said...

0.121212...........=4/33

AtTIDuDe GirL XxX said...

0.17171717... is a recurring decimal.
..
100x 0.17= 17.171717...
-
1x 0.17= 0.17
= 99x 0.17= 17
..
0.17 = 17/99

AtTIDuDe GirL XxX said...

eh, the attitude girl that post is pearlyn's post. i am using my cousin's account to post, because i cannot post using my name.

geng fa :( said...

For example an recurring number
(0.333333...),this is recurring numbers so it can be expressed as a fraction for example (0.11111.....) is also a recurring decimal it can be expressed as 1/9.
XD

Anonymous said...

Fraction Decimal Overline Dots Brackets
1⁄9 0.111… 0.1 0.(1)
1⁄3 0.333… 0.3 0.(3)
2⁄3 0.666… 0.6 0.(6)
1⁄7 0.142857142857… 0.142857 0.(142857)
1⁄81 0.012345679…0.012345679(0.012345679)
7⁄12 0.58333… 0.583 0.58(3)

Kellyyy ;DD said...

hmm... lets see ;D

A reccuring decimal is a decimal (duh! ;D) that repeats numbers in a certain form , eg. 0.369369369369369369 .... etc.

it will equal to : 369/999 :D

bahh T__T *random message*

Krystal said...

Hello! Krystal here i dont know how to put user name psps... Uhhh not really sure I understand the concept so I trying only...
The recurring decimal I want to use is 0.15151515...
To change a recurring decimal into a fraction,we should see the amount of numbers being repeated. For the number I am using ,it has two recurring decimals so we should take 10 to the power of 2
0.1515151515x100=15.15151515
0.1515151515x1=0.1515151515
15.15151515-0.151515151515=15
As we have a ''balance'' of 99x15 ,we ''use'' it as 15/99
=5/33

Jia Jun said...

0.03030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030...

Jia Jun said...

0.03030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303030303003030303003030303030303030303030303=1/33

Jia Jun said...

0.03030...

=1/33

I am Ren Kai
This is an example of a repeating decimal
0.583333333...=7/12

Anonymous said...

0.123412341234.......

1x(0.1234.......)=0.1234.......
10000x(0.1234....)=1234.1234......
________________________________

10000-1=9999 1234

1234/9999
so recurring are real number
by Brian

gonner said...

my no. is 0.105105105....
1000x0.105105105....
=105.105105105
1x0.105105105...
=0.105105105...
105.105105105...-0.105105105...
=105
999x0.105105105....
=105/999
_________________________________
20.0103030303.....
0.01=1/100
0.0303030303....
100x0.03030303
=3.03030303....
1x0.03030303...
=0.03030303....
99x0.0303030303...
=3/99
=1/33
1/3300+33
=34/3300
=17/1650

Yi xuan said...

gonner is me yixuan

anthony said...

one of the reccuring decimals is 0.407407407407.... which is equal to 11 or 11/27
--
27

Ng Jing Hang said...

I am UzumakiIchigo....

Li Cheng said...

An example of a recurring number:9.0909090909...

This is the trick to find out what fraction that repeating number is equal to.

First, count the number of digits in the repetend. if the repetend is 09, the number of digits is 2.
Next multiply your repeating decimal by a power of 10.

If we multiply the repeating decimal by a power of 10 in this way, we end up with a decimal which has the repetend to the LEFT of the decimal point, and the same repeating decimal we started out with to the right of the decimal point.

After we multiply by this appropriate power of 10, we get the sum of an integer(which is numerically equal to whatever
the repetend was) and the repeating decimal we started out with. If we let x be the repeating decimal we started out with, we find:

Let x be the repeating decimal we started out with, we find:
If x = .0909..., you can see that we get 100x = 9 + x, or
99x = 9, or x = 9/99 = 1/11.

brantonfoo said...

when you divide a no. and the answer has a recurring decimal,you take the numbers that are repeated and classify them as one set. e.g 0.33333......you take the number 3.then to make the recurring decimal 0.33333....to a fraction,you times the recurring decimal by 10 as the recurring number is a singe digit.thus,the answer is 3.333333...to make it a whole number,you must minus 0.3333..to get the whole number as 3.

3.33333..=10 times of 0.3333....
3=9 times of 0.333333
=3/9
=1/3

said...

A recurring decimal usually is

either a imaginary or real number,

such as (0.313131...). Logically,

such a number cannot be

represented by a decimal, so it is

expressed through fractions(31/100)

said...

Oops. What did I do?

rebecca♥nyh said...

how but 0.24565656565656.... how do i do?