A decimal expression is a rational number if it can be represented as a ratio of two integers, p/q where q > 0.
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 of the rational form is the old original string including one lot of the repeated digits minus the original string with none of the repeating digits.
The denominator of the rational form is 10^c*(10^d - 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.
Wiki User
∙ 6y agoYes, a rational number can be a repeating decimal. A repeating decimal is a decimal in which one or more digits repeat infinitely. For example, 1/3 is a rational number that can be written as the repeating decimal 0.333...
A terminating decimal is a rational number. A non-terminating, repeating decimal is a rational number. A non-terminating, non-repeating decimal is an irrational number.
Repeating decimals are always rational.
Any rational number is either a repeating decimal, or a terminating decimal.
It is either a terminating decimal or a repeating decimal.
Yes, a rational number can be a repeating decimal. A repeating decimal is a decimal in which one or more digits repeat infinitely. For example, 1/3 is a rational number that can be written as the repeating decimal 0.333...
Yes. Any terminating decimal is a rational number. Any repeating decimal also.
A terminating decimal is a rational number. A non-terminating, repeating decimal is a rational number. A non-terminating, non-repeating decimal is an irrational number.
No. A rational number is any terminating numeral. A repeating decimal is irrational.
Any rational number is either a repeating decimal, or a terminating decimal.
Repeating decimals are always rational.
Yes.
Since 2.33333... is a repeating decimal (or recurring decimal), it is a rational number.
No. It is a rational number. Any repeating decimal or terminating decimal is rational.
All repeating decimals are rational numbers. Not all rational numbers are repeating decimals.
Not always because any decimal that can be expressed as a fraction is a rational number as for example 0.33333.....repeating can be expressed as 1/3 which is a rational number
It is either a terminating decimal or a repeating decimal.