Question

Consider the rational number 3/11 (A What are the values of a and b in a)‾b when you use divisison to find the decimal form?

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2. linhdan
The decimal form of this rational number is .
Step-by-step explanation:
a) Let  a rational number. From statement we understand that  represents the numerator, while  corresponds with the denominator of the rational number. Hence,  is 3 and  is 11.
b) The decimal form is obtained by dividing  by , 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 .