logo for solving-math-problems.com
leftimage for solving-math-problems.com

Decimals with Repeater as a Fraction

by Campbell
(Sydney, Australia)











































Turn a decimal into a fraction

rewrite 0.12 repeater as a fraction

Keep in mind that both a decimal and a fraction stand for part of a whole integer.

You can visualize this by thinking about cutting a wedge from an apple. The wedge (which can be represented by a decimal or a fraction) is a part of the apple, but not the whole apple.

Comments for Decimals with Repeater as a Fraction

Click here to add your own comments

Jul 11, 2013
Decimal – Fraction – Equivalence
by: Staff


Answer

Part I

If 0.12 is not a repeating decimal, you can solve the problem like this:

Since there are two numbers to the right of the decimal, the fraction is:

12/100

Or (the reduced form)

3/25


However, if 0.12 is does represent a repeating decimal, it should look like this:

.(a)(a)(a)...

“a” is called the “repetend”

0.1212121212 . . .



Follow the next few steps to turn this repeating decimal into a fraction


Multiply the repeating decimal by 100.


You should use the number 100 because it will shift the decimal point exactly two digits. This is because the number which repeats itself is exactly two digits.

(If the number which repeats itself was 3 digits, such as .123123123 . . ., then you would multiply by 1000 . . . and so on.)


Let x stand for the repeating decimal

x = 0.1212121212 . . .


100x = 100 * (0.1212121212 . . .)

100x = 12.1212121212 . . .


 Convert Repeating Decimal to fraction:  

let x = repeating decimal

multiply x by 100






---------------------------------------------------------------------------

Jul 11, 2013
Decimal – Fraction – Equivalence
by: Staff

---------------------------------------------------------------------------



Part II


Subtract 1x from 100x



100x = 12.1212121212 . . .

-x = - 0.1212121212 . . .

-------    ----------------------

99x = 12



subtract x from 100x






Divide each side of the equation by 99

99x = 12

99x / 99 = 12 / 99

x = 12 / 99

or, in its reduced form

x = 4 / 33



divide each side of the equation by 99







---------------------------------------------------------------------------

Jul 11, 2013
Decimal – Fraction – Equivalence
by: Staff


---------------------------------------------------------------------------



Part III


the final answer is:


0.1212121212 . . . = 4 / 33



convert repeating decimal 0.121212… to a faction – final answer







Thanks for writing.

Staff
www.solving-math-problems.com


Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Math Questions & Comments - 01.



Copyright © 2008-2015. All rights reserved. Solving-Math-Problems.com