How to find the fraction for repeating decimals,indian cell phone reverse lookup jamaica,qatar airways phone number in china,canada immigration pearson airport phone number - PDF Books

With Instructables you can share what you make with the world, and tap into an ever-growing community of creative experts. Building bigger numbers out of smaller numbers is one of the grand traditions of mathematics. Decimal numbers with repeating decimals appeared in our universe soon after long division was invented.
If you happen to start with a number in decimal form, this process of finding a mixed fraction is much, much, easier.
You might have noticed the denominators of the fraction forms of these repeating decimal numbers usually have a whole bunch of nines in them. The trick here is to expand the decimal number as a the sum of its integer part, the non-repeating part, and whatever is left over. Next I want to multiply the numerator and the denominator by a power of 10 large enough to shift the fractional part of the decimal into integer territory.

To figure out how large of a power of 10 I will need, I count the number of digits to the right of the decimal point, excluding trailing zeros.
Now if you want to, you can reduce this fraction, so that the numerator and denominator are coprime. By the way, for factoring that numerator and denominator, I got a little help from a close, personal friend of mine, Octave, the numerical problem solving application I mentioned in the introduction.
A handy way to remember the decimals in sevenths (mentioned in the 7th step) is 7 14 28 5.. One thing I forgot to mention in this instructable is the cultural phenomena of marketeers who offer their wares with prices ending in nines, e.g. The other day I found a beautiful 1.999 in the wild, and I decided to take a picture of this and add it to Step 10. Some students get their first look at manipulating equations when they learn how to convert a repeating decimal to its corresponding fraction (rational numbers yield terminating decimals, or non-terminating repeating decimals).

It's kind of a neat party trick (for very specific geekly parties) to quote percentages of stuff that there happens to be seven of.
The manipulation is done by multiplying the equation by the right power of 10 to shift the digits, and then subtracting off the original equation.Perhaps you have a more complicated repeating decimal that you want to fractionalize. The procedure remains essentially the same: obtain two equations that have the same "decimal part" that can be eliminated by subtracting. Which fractions terminate, and which keep going?A fraction can sometimes give us a terminating decimal, and sometimes a repeating decimal.
For a non-terminating repeating decimal, questions about the length of the repeating part are harder to answer.

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