Answer:
The decimal form of this rational number is  .
.
Step-by-step explanation:
a) Let  a rational number. From statement we understand that
 a rational number. From statement we understand that  represents the numerator, while
 represents the numerator, while  corresponds with the denominator of the rational number. Hence,
 corresponds with the denominator of the rational number. Hence,  is 3 and
 is 3 and  is 11.
 is 11. 
b) The decimal form is obtained by dividing  by
 by  , we presented the step needed to determine the decimal form:
, we presented the step needed to determine the decimal form:
i) Multiply the numerator by 10:
Dividend: 30/Divisor: 11/Known result: 0. /Residue: N/A
ii) Multiply the divisor by 2 and subtract from the dividend:
Known result: 0.2 /Residue: 8
iii) Multiply the residue by 10:
Known result: 0.2 /Residue: 80
iv) Multiply the divisor by 7 and subtract from the residue:
Known result: 0.27 /Residue: 3
v) Multiply the residue by 10:
Known result: 0.27 /Residue: 30
vi) Multiply the divisor by 2 and subtract from the residue:
Known result: 0.272/Residue: 8
vii) Multiply the residue by 10:
Known result: 0.272 /Residue: 80
viii) Multiply the divisor by 7 and subtract from the residue:
Known result: 0.2727/Residue: 3
We have notice that the decimal form of  is a periodical decimal number. Hence, we conclude that decimal form of this rational number is
 is a periodical decimal number. Hence, we conclude that decimal form of this rational number is  .
.