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Yes, it can.

Q: Can decimal that has repeating digits after the decimal point be converted into a fraction?

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No... you can write it to any number of decimal places.

There are three different situations, corresponding to the three types of decimal numbers: terminating, repeating and those which are neither terminating nor repeating. Terminating: If the decimal number has d digits after the decimal point, then rename it as a fraction whose numerator is the decimal number without the decimal point, and the denominator is 10d or 1 followed by d zeros. For example, 34.567 d = 3 so the denominator is 1000. and the fraction is 34567/1000. Repeating: Until you become expert at this I suggest you do this in two stages (using c and d separately). Suppose there are c digits after the decimal place where the digits are non-repeating, after which you get a repeating pattern of a string of d digits. Then the numerator is the old original string including one lot of the repeated digits minus the original string with none of the repeating digits. The denominator is 10c*(10d - 1), which is a string of d 9s followed by c 0s. For example 123.26159159… There are 2 digits, "26", after the decimal point before the repeats kick in so c = 2, and the repeating string "159" is 3 digits long so d = 3. So the numerator is 12326159 – 12326 = 12313833 and the denominator is 99900 Therefore the fraction is 12313833/99900. Non-terminating and non-repeating: There is no way to get a proper fraction since, by definition, this is an irrational number. The best that you can do is to round it to a suitable number of digits and then treat that answer as a terminating decimal. In all cases, you should check to see if the fraction can be simplified.

If both digits are repeating then as a fraction it is 37/99

It is placed over one length of repeating decimal digits.

If it is a terminating decimal, count the number of digits after the decimal and call it x. Put those digits over 10^x and reduce. For example, if the fraction is 0.84, x is 2, so 84/10^2 = 84/100 = 21/25■ If it is a repeating decimal, put the repeating portion over (10^x)-1. If the fraction is 0.848484..... put 84/(100-1) = 84/99 = 28/33■

Related questions

No... you can write it to any number of decimal places.

The answer depends on the repeating string and also on other digits after the decimal point before the repeating string starts.

A repeating decimal fraction.

You do a long division, adding decimal digits until you get a remainder of zero (terminating decimal) or a repeating pattern of decimal digits.

4111 is an integer and so there is no sensible way to convert it into a repeating decimal.

I assume you mean "repeating decimal". Yes. For example, 1/6 = 0.166666... after that, the digit "6" repeats over and over again. In other cases, it is more than one digit that repeats, over and over. Note that at first there may be other digits, that don't repeat later on.In general, any fraction (with integers on top and bottom), if converted into a decimal, will eventually start repeating. Conversely, any repeating decimal can be converted into a fraction.

The fraction 1/7 has the decimal value 0.142857142857142857..... The six digits 142857 keep repeating.

A decimal fraction is said to be repeating if, after a finite number of digits, there is a string of a finite number of digits which repeats itself for ever more.For example,1537/700 = 2.19571428571428...The first three digits in the decimal representation are not part of the repeating pattern. After that, however, the string "591428" repeats endlessly.

If you know what rational fraction it represents then, if the denominator in the fraction's simplest form has any prime factor other than 2 and 5, then it is a repeating decimal and if not it is terminating.Otherwise you need to examine the digits of the decimal representation in detail. Remember though, that the repeating string could be thousands of digits long (or even longer).

A repeating fraction is a decimal representation of a number in which a string of numbers repeats itself endlessly. The repeating string may start after a finite number of non-repeating digits. For example, 29/132 = 0.21969696... repeating. The repeated sequence is [96] which starts after two digits.

You mean fraction. Fractor isn't a word at all. To convert a repeating decimal to a fraction, first multiply the decimal by 100. Ignore the digits on the right side of the decimal point and keep the number that is on the left side of the decimal point. Divide this number by 99 and simplify if necessary to get the fraction.

The following procedure is for converting a general repeating decimal, that is, one which does not start repeating straight away. Until you become expert at this I suggest you do this in two stages (using c and d separately). Suppose there are c digits after the decimal place where the digits are non-repeating, and then you get a repeating pattern of a string of d digits. Then the numerator is the old original string including one lot of the repeated digits minus the original string with none of the repeating digits. The denominator is 10^c*(10^d - 1), which is a string of d 9s followed by c 0s.Example123.26159159… There are 2 digits, "26", after the decimal point before the repeats kick in so c = 2, and the repeating string "159" is 3 digits long so d = 3.So the numerator of the fraction is 12326159 – 12326 = 12313833and the denominator is 99900Therefore the fraction is 12313833/99900.