We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

What common fraction (that is, a fraction reduced to its lowest terms) is equivalent to \(.3\overline{25}\) ?

tertre Dec 23, 2017

#1**+1 **

For this one

1) Ignore the decimal

2) Take the "whole" and subtract the non-repeating part = 325 - 3 = 322

3) Put this over a number that has the same number of 9's as the repeating part = 99, followed by the same number of 0's as the non-repeating part = 0

4) So we have

322 / 990 = 161 / 495

Verify for yourself that this is equal to the required decimal

CPhill Dec 23, 2017

#3**+1 **

I have not seen a interminably repeating decimal be converted into a simplified fraction in the fashion Cphill described above, but I will present to you an alternate method. On further review, though, the method I have below appears to prove Cphill's method.

\(x=0.3\overline{25}\) | Firstly, I set the repeating decimal equal to a variable. I will use the standard choice, x. |

\(x=0.325252525...\) | A few more decimal places should be written out so that the method is clear. |

Now, multiply x by a factor of ten such that the repeating portion lines up with the first line.

\(10x=3.25252525...\\ \hspace{5mm}x=0.325252525...\) | Notice how the repeating portion does not line up here, so this is not the correct multiple of ten. Let's multiply both sides by ten again. |

\(100x=32.525252525...\\ -(\hspace{1mm}x=\hspace{2mm}0.325252525...)\) | Look at this! Notice how the repeating portion of both equations line up perfectly. Now, subtract the two equations from each other. |

\(99x=32.2\) | Now, solve for x. |

\(x=\frac{32.2}{99}\) | Apply a multiplication of 10/10 to simplify the fraction. |

\(x=\frac{322}{990}=\frac{161}{495}\) | |

TheXSquaredFactor Dec 23, 2017

#5**0 **

I appreciate it!. I really like it when people get together and share ideas. Great website, continue the good work!. Either way, great web and I look forward to seeing it grow over time. Thank you so much. |=>super smash flash 2 |=>bloons tower defense 5

rebeccahic Dec 25, 2017