find the sun of the digits of the denominator in the simplest form of the below given rational number 288/468
Answers
Answer:
Remember that if the denominator of a rational number contains only 2 or 5, multiples of 2 or 5 or a combination of both, then the rational number will be a 'terminating' decimal.
A rational number with denominator other than 2 and 5 or its multiples will be a 'non-terminating recurring' decimal.
(i) The given fraction is. Since the prime factorization of 5 which is is in the form .
So it has terminating (T) decimal.
(ii) The given fraction is .
The denominator of the given rational number is 7, which can be factorized as. Since the denominator is not of the form. Hence, the rational number has a recurring (R) decimal representation.
(iii) The given fraction is.
The denominator of the given rational number is 49, which can be factorized as. Since the denominator cannot be expressed in the form. Hence, the rational number has a recurring (R) decimal representation.
(iv) The given fraction is.
The denominator of the given rational number is 40, which can be factorized as . Since the denominator of the given fraction is in form. Hence, the rational number has a terminating (T) decimal representation.
(v) The given fraction is.
The denominator of the given rational number is 64, which can be factorized as . Since the denominator of the given fraction is in the form. Hence, the rational number has a terminating (T) decimal representation.
(vi) The given fraction is.
The denominator of the given rational number is 75, which can be factorized as. Since the denominator of the given fraction is not of the form. Hence, the rational number has a recurring (R) decimal representation.
(vii) The given fraction is.
The denominator of the given rational number is 125, which can be factorized as. Since the denominator of the given fraction is in form. Hence, the rational number has a terminating (T) decimal representation.
(viii) The given fraction is.
The denominator of the given rational number is 213, which can be factorized as . Since the denominator of the given fraction is not of the form. Hence, the rational number has a recurring (R) decimal representation.
(ix) The given fraction is.
The denominator of the given rational number is 160, which can be factorized as. Since the denominator of the given fraction is in form. Hence, the rational number has a terminating (T) decimal representation.
(x) The given fraction is, it is in its lowest form, i.e., there is no common factor other than 1 in the numerator and the denominator. So, it is a rational number.
The denominator of the given rational number is 75, which can be factorized as. Since the denominator of the given fraction is not of the form. Hence, the rational number has a recurring (R) decimal representation