Question

Consider the rational number 3/11 a. What are the value of a and b in a divide by b when you use division to find the decimal form b. What is the decimal form for 3/11

Answer 1

Answer:

The decimal form of this rational number is $0.\overline {27}$.

Step-by-step explanation:

a) Let $\frac{a}{b}$ a rational number. From statement we understand that $a$ represents the numerator, while $b$ corresponds with the denominator of the rational number. Hence, $a$ is 3 and $b$ is 11.

b) The decimal form is obtained by dividing $a$ by $b$, 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 $\frac{3}{11}$ is a periodical decimal number. Hence, we conclude that decimal form of this rational number is $0.\overline {27}$.