Results 1 to 4 of 4

Math Help - rational number representation

  1. #1
    Newbie
    Joined
    Feb 2008
    Posts
    6

    rational number representation

    I have a question that I can't recall how to do. Here it is.

    Determine and state the rational number representation for the following decimal. Put the rational number in lowest terms.

    ( line is above the numbers
    1485) ____

    n= 0. 0 1485

    n=

    I would greatly appreciate your assistance.

    Thank you.

    Melissa
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Reckoner's Avatar
    Joined
    May 2008
    From
    Baltimore, MD (USA)
    Posts
    1,024
    Thanks
    75
    Awards
    1

    Smile

    Quote Originally Posted by mdoodles View Post
    I have a question that I can't recall how to do. Here it is.

    Determine and state the rational number representation for the following decimal. Put the rational number in lowest terms.

    ( line is above the numbers
    1485) ____

    n= 0. 0 1485
    Here is one way to do it:

    n=0.0\overline{1485}

    So,

    <br />
\begin{tabular}{rcr@{.}l}<br />
10000n & = & 148&514851485...\\<br />
- n & = & 0&014851485...\\<br />
\hline<br />
9999n & = & 148&5\\<br />
\end{tabular}<br />

    Now,

    9999n = 148.5

    \Rightarrow n = \frac{148.5}{9999} = \frac{1485}{99990}

    Then reduce. Alternatively, you can represent the number as an infinite series.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2008
    Posts
    6
    Thank you so much. I remember we did this in class but I couldn't find it in my notebook. I just found it in my other notebook. It was driving me crazy. Thank you so much for your assistance. I appreciate it.

    Melissa
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Reckoner's Avatar
    Joined
    May 2008
    From
    Baltimore, MD (USA)
    Posts
    1,024
    Thanks
    75
    Awards
    1

    Smile

    Quote Originally Posted by mdoodles View Post
    Thank you so much. I remember we did this in class but I couldn't find it in my notebook. I just found it in my other notebook. It was driving me crazy. Thank you so much for your assistance. I appreciate it.

    Melissa
    No problem. In case you are still interested, here is how to do it with infinite series:

    n=0.0\overline{1485}=0.01485+\frac{0.01485}{10000}  +\frac{0.01485}{10000^2}+\cdots=\sum_{n=0}^\infty \frac{0.01485}{10000^n}

    =\frac{1485}{10^5}\sum_{n=0}^\infty\left(\frac{1}{  10^{4n}}\right)=\frac{1485}{10^5}\sum_{n=0}^\infty  \left(\frac{1}{10^4}\right)^n

    =\frac{1485}{10^5}\left(\frac1{1-\frac1{10^4}}\right)=\frac1{\left(\frac{9999}{10^4  }\right)}

    =\frac{1485}{10^5}\left(\frac{10^4}{9999}\right)=\  frac{1485}{99990}=\frac{3^3\cdot5\cdot11}{2\cdot3^  2\cdot5\cdot11\cdot101}=\frac3{202}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Number representation problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: August 18th 2011, 03:06 AM
  2. Replies: 2
    Last Post: May 3rd 2011, 04:22 PM
  3. Replies: 4
    Last Post: April 28th 2011, 07:20 AM
  4. Replies: 5
    Last Post: October 7th 2008, 01:55 PM
  5. [SOLVED] number representation
    Posted in the Math Software Forum
    Replies: 1
    Last Post: January 19th 2008, 11:43 PM

Search Tags


/mathhelpforum @mathhelpforum