Express the following in the form where p and q are integers and q ≠ 0. - Wired Faculty

Polynomials

Question

Express the following in the form $straight p over straight q$ where p and q are integers and q ≠ 0.
$left parenthesis straight i right parenthesis space 0. top enclose 6$

Solution

Let    $straight x space equals space 0. top enclose 6 equals 0.6666.....$
Multiplying both sides by 10 (since one digit is repeating), we get
10x = 6.666 .......
$rightwards double arrow$ 10x = 6 + 0.6666 .....
$rightwards double arrow$ 10x = 6 + x
$rightwards double arrow$ 10x - x = 6
$rightwards double arrow$ 9x = 6
$rightwards double arrow space$    $straight x space equals space 6 over 9$
$rightwards double arrow$    $straight x space equals space 2 over 3$
Thus,    $0. top enclose 6 equals 2 over 3$
Here p = 2
q = 3 ( $not equal to 0$ )

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Polynomials

Express the following in the form $straight p over straight q$ where p and q are integers and q ≠ 0.
$left parenthesis straight i right parenthesis space 0. top enclose 6$

Some More Questions From Polynomials Chapter

Find two rational numbers between 0.1 and 0.2.

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