:: : Yes, I'm a great fan of the continued fraction method for " approximations ", but if you know the period of a repeating decimal the approach suggested by the series is better . talk ) 17 : 14, 5 November 2008 ( UTC)
32.
So this particular repeating decimal corresponds to the fraction 1 / ( 10 " n " & minus; 1 ), where the denominator is the number written as " n " digits 9 . Knowing just that, a general repeating decimal can be expressed as a fraction without having to solve an equation.
33.
So this particular repeating decimal corresponds to the fraction 1 / ( 10 " n " & minus; 1 ), where the denominator is the number written as " n " digits 9 . Knowing just that, a general repeating decimal can be expressed as a fraction without having to solve an equation.
34.
Every terminating decimal representation can be written as a decimal fraction, a fraction whose divisor is a 0.999 & } } and 1.584999 & } } are two examples of this . ( This type of repeating decimal can be obtained by long division if one uses a modified form of the usual division algorithm .)
35.
If you start with, " What is 32 / 7 you are going to get monsters like 4.571428571428 and unless that's what you want ( to demonstrate the repeating decimals of numbers divided by 7 ) it's a monster to deal with gradewise . talk ) 22 : 29, 20 October 2014 ( UTC)
36.
It follows that any repeating decimal with period " n ", and " k " digits after the decimal point that do not belong to the repeating part, can be written as a ( not necessarily reduced ) fraction whose denominator is ( 10 " n " & minus; 1 ) 10 " k ".
37.
For arithmetic, Bhrat + K [ c G a gives several algorithms for whole number multiplication and division, ( flag or straight ) division, fraction conversion to repeating decimal numbers, calculations with measures of mixed units, summation of a series, squares and square roots ( duplex method ), cubes and cube roots ( with expressions for a digit schedule ), and divisibility ( by osculation ).
38.
A decimal may be a terminating decimal, which has a finite fractional part ( e . g . 15.600 ); a repeating decimal, which has an infinite ( non-terminating ) fractional part made up of a repeating sequence of digits ( e . g . 5.123 144 ); or an infinite decimal, which has a fractional part that neither terminates nor has an infinitely repeating pattern ( e . g . 3.14159265 . . . ).
39.
I am basing this on the rule that, to convert a repeating decimal to a fraction, you just take only the group of numbers that repeats over a number of " 9's " equaling the number of numbers that repeats, i . e ., . 732732 . . . ( Repeating ) = 732 / 999 . And, if so, then what number comes right before . 9 ( Repeating ) in terms of size ? Preceding contribs ) 20 : 10, 8 November 2007 ( UTC)
40.
:: : : : The worst case scenario is going to be an irrational whose decimal remainder is something like . 213456, which will lie half way between our options of . 142857 and . 285714-- in which case we can change from fractions over 7 to more suitable higher prime denominators such as 17 with its 16 repeating decimals : 1 / 17 = 0.0588235294117647 and its 16 more precise . 05, . 11, . 17, . 23, . 29, etc . ) optional remainders.
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