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I am tutoring a supersmart, high-SES seventh grader, and his class is converting repeating decimals to fractions using algebra. This is in a Chicago public school in a "gentrified" neighborhood.
Now, I have been happily converting repeating decimals of the type 0.3333..., 0.6666..., 0.232323... and 0.753753753... for a while using algebra. I was initially thrown when the decimals he was given for homework were of the type 0.244444..., 0.3020202... and 0.4213213213. I hadn't encountered those before.
I thought some KTM readers might enjoy trying their hands on those.
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6 comments:
You know, I don't remember at all doing this when I was growing up. I've never had a need to do this except just recently with my son's homework, but not problems like 0.2444... It's strange coming across something that you've never seen before, and probably should have.
I assume you pre- ... oops, I'll wait.
Ugly repeating decimals:
"About as much fun as watching a documentary with your parents."
Yesterday my daughter was converting fractions to repeating decimals. She'd likely agree that using algebra to do the inverse and applying Euler's Forumla would have been more fun.
The algorithm mentioned on that site is properly called the Euclidean Algorithm, not Euler's Formula. (I have sent a correction to the site.)
It's a better method than factoring for reducing fractions (at least when the numerator and denominator are large), and a lot more fun too.
How about:
Let N=0.2444...
100N = 24.4444...
-10N = 2.4444...
__________________
90N = 22
N = 22/90 or 11/45 reduced
Same idea with that last example, only you have to use 10,000N to finally arrive at 1403/3330
Saxon Math does tons of these.
In Algebra 2, I think.
.4213213213...:
Chop off the non-repeating part, and leave it for last:
.4+.0213213213213...
Move the decimal place where you want it to be:
.4+.1*.213213213...
Now do the repeating bit using your favorite method
[work here]
.4+.1*(213/999)
Do the fraction stuff:
4/10+(1/10)*(213/999)
=4*999/9990+213/9990=4209/9990
Simplify to taste:
=1403/3330
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