Convert recurring decimal to fraction?
924084
Start with the fixed part... 2.1 is 21/10.\n\nThe rest of the number is 0.036363636...\nLet's call that x.\n\nx = 0.036363636...\nNotice what happens if you multiply by 100.  I picked 100 because there are two repeating decimals.  If there were 1 you would pick 10, if 3, you would pick 1000, if 4 pick 10000, etc.\n100x = 3.6363636...\n.......x = 0.0363636...\n\nSubtract and the repeating decimals are cancelled:\n99x = 3.6\n\nMultiply by 10 to get rid of the last remaining decimal:\n990x = 36\n\nNow solve for x:\nx = 36/990\n\nNow you just need to add your two fractions:\n21/10 + 36/990\n\nGet a common denominator:\n21*99/990 + 36/990\n\n= (2079 + 36)/990\n= 2115/990\n\nNow reduce:\n= 235 / 110\n= 47 / 22\n= 2 3/22\n\nSo your answer is 2 and 3/22.\n\nYou can also do this in one step, without having to do the two parts:\n100x = 213.63636...\n.......x = .....2.13636...\n\nSubtracting:\n99x = 211.5\n\nMultiply by 10 to remove the decimal:\n990x = 2115\n\nSolve for x:\nx = 2115/990\nx = 47/22\nx = 2 3/22\n\nA final way, if you now understand the underlying math is to just do the following:\n\nPull out the part in front of the decimal (2)... just keep that for later.\n\nThe remaining part is 0.136363636... \nSince we have two repeating decimals, use two nines (99).  However, since it is offset by one fixed digit, add a trailing zero (990).\nTake the fixed digit (1) and subtract it from your number (136, ignoring anything but the first repeat).  This leaves 135.\n\nSo the fraction should be 135/990.  This reduces to 3/22.\n\nSo it becomes 2 and 3/22.\n\nAlways check that the final result makes sense.  Obviously the first part of the mixed fraction should match the decimal (2) and it does.  If you put 3/22 in your calculator, you get 0.1363636...\n\nThere's 3 different methods and they all give you 2 and 3/22.
986357
Take a=0.080808. I will assume that the last 08 digits are repeated. This process will work for decimal to fraction conversions\n\na=0.08080808 etc\n\nMultiply both sides by 100\n\n100a = 8.08080808 etc\n\nSubtract first from the second\n\n99a = 8\n\nTherefore a = 8/99 = 0.08080808 etc\n\nTry the other ones
109233
convert a % to a fraction by putting the number over 100.  For example, 34% is 34/100.  which is also .34 as a decimal.
960965
fractions into decimals\n\neasy way is 7/100 \ndivide 7 by 100 and you will get 0.07\n\ndivde mix fractions like 2 5/8\nchange into improper fraction 21/8\nthen divde 21 by 8 and you will get 2.625
1016721
actually, I use BCD for decimals\n\n0.264\n0010 0110 0100 (BCD)
561531
9% easy way to convert decimals to percentages is move the decimal period to the right two places
354488
To convert a fraction to decimal using a calculator, its just the top number (numberator) divided by the bottom number (denominator).\n\n1 ÷ 4 = 0.25\n\nTo convert it without a calculator, you can use equilavent fractions, which works for some easy denominators. Just change the denominator to a power of 10 (10,100,1000,...) by multiplying the top and bottom by the same amount, which keeps the same value of the fraction.\n\n1/4 = 1*25 / 4*25 = 25/100 = 25 hundredths\n\n25 hundredths ends in the hundredths column, so 0.25\n(thats the same as 2 tenths and 5 hundredths)\n\nYou can also work out any fraction into a decimal using long division, just proceed past the decimal as normal, putting in extra 0's\n\n1 ÷ 4 = 4 into 1 = 4 into 1.00\n\n4 ) 1.00\n\n4 into 1 goes 0 remainder 1\n4 into 10 goes 2 remainder 2\n4 into 20 goes 5\n\n0.25, keeping the decimal point in the same place\n\nThis always works, although you will need to decide when to stop for a repeating decimal such as 1/3\n\n3 ) 1.0000...\n\n3 into 1 goes 0 remainder 1\n3 into 10 goes 3 remainder 1\n3 into 10 goes 3 remainder 1\n3 into 10 goes 3 remainder 1\n3 into 10 goes 3 remainder 1\n.\n.\n.\n\n1/3 = 0.33333...
369365
move the decimal point to the left 9 spaces.\n.000000004.
998641
The answers above are great for cases where the repeating part is right at the beginning as shown in the examples below:\n\n0.22222222... = 2/9\n0.54545454... = 54/99\n0.298298298... = 298/999\n0.142857142857... = 142857/999999 = 1/7\nDivision by 9s causes the repeating pattern.  Notice how the number of 9s is equal to the length of the repeat.  Don't forget to reduce the fraction if you can.\n\nThere are other cases though that you asked about.  For example if there are zeroes preceeding the repeating decimal, then you need to convert as follows:\n\n0.022222222... = 2/90\n0.099999999... = 9/90 = 1/10 (same as 0.1 by the way)\n0.00054545454... = 54/99000\n0.00298298298... = 298/99900\nNote that adding zeroes to the denominator adds an equivalent number of zeroes before the repeating decimal.\n\nTo convert a decimal that begins with a non-repeating part, such as 0.21456456456456456..., to a fraction, write it as the sum of the non-repeating part and the repeating part.\n  0.21 + 0.00456456456456456...\n\nNext, convert each of these decimals to fractions. The first decimal has a divisor of power ten. The second decimal (which repeats) is converted according to the pattern given above.\n  21/100 + 456/99900\n\nNow add these fraction by expressing both with a common divisor\n  20979/99900 + 456/99900\n\nand add.\n  21435/99900\n\nFinally simplify it to lowest terms\n  1429/6660\n\nand check on your calculator or with long division.\n= 0.2145645645...\n\nThat should cover all the cases you might have.
290434
the answer is 6162/990\n\nTo figure this out, multiply the original number by 1000 (so that you only have the repeated number as a decimal.\nThen multiply the number by 10 so that the repeated number is also in the decimal.\n\n1000x = 6224.2424\n10x   = 62.2424\nNow subtract the two...\n\n990x = 6162.00\nsolve for x ->  x=6162/990\n\nnow check it on your calculator.
1167572
The answer is:\n115740.74074074074074074074074074 etc.\n\nthe 740s after the decimal repeats forever.
252300
I think this is otherwise known as recurring numbers. This occurs when you have an irrational number. The number is usually a fraction that does always has a remainder, but this remainder when written in the decimal is somewhat repeated. In other words thre is a sequence. An example is 0.722372237223. The numbers 7223 are recurrent.A number which does have a lot of numbers in its decimal but doesnt have recurrent numbers is e
109858
5/3 is 1 and 2/3. It will give you a nonterminating decimal. 1.6666666666666666666666666666666666666666 66666666666666666666666666666666666666666666 66666666666666666666666666666666666666666666 66666666666666666666666666666666666666666666
660791
You just switch the top number and bottom number\n\nhttp://www.mathleague.com/help/fractions/fractions.htm#reciprocal
194748
21  9/10\n\nand this is why: http://www.webmath.com/cgi-bin/fraction.cgi?decimal=21.45&op=to_fraction&back=dec2fract.html
33410
Round nothing.\n365.0/7.00 = 52.14 + in a regular year\n366.0/7.00 = 52.28 + in a leap year.
704342
You would first convert it to a fraction.\n\n.5555... = 5/9\n\nIn general, when you have a repeating decimal, just put the repeating portion over an equivalent number of nines.  So .5555... = 5/9\n\n(As another example, .1818... = 18/99 = 2/11, and .135135... = 135/999 = = 15/111 = 5/37)\n\nSo once you convert the repeating number to a fraction you have 30 5/9%\n\nIn words this is "thirty and five-ninths percent"