Answer:
The decimal form of this rational number is [tex]0.\overline {27}[/tex].
Step-by-step explanation:
a) Let [tex]\frac{a}{b}[/tex] a rational number. From statement we understand that [tex]a[/tex] represents the numerator, while [tex]b[/tex] corresponds with the denominator of the rational number. Hence, [tex]a[/tex] is 3 and [tex]b[/tex] is 11.
b) The decimal form is obtained by dividing [tex]a[/tex] by [tex]b[/tex], 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 [tex]\frac{3}{11}[/tex] is a periodical decimal number. Hence, we conclude that decimal form of this rational number is [tex]0.\overline {27}[/tex].
