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?

Answers

  1. Answer:
    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 .

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