Question

II. Express the following in the form p/q, where p and q are integers and q≠0

0.6​

Answer 1

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$\sf{0.6 = 0.666..}$

$\sf{Let \: x \: = 0.666...(1) }$

• Here only one digit is repeating so multiply by 10 on both sides.

$\sf{10 × x = 10 \times 0.666....}$

$\sf{10x = 6.666....(2)}$

• On subtracting equation 1 from equation 2

$\sf{10x- x = 6.666.... - 0.666...}$

$\sf{9x = 6}$

$\sf{X = 9/6 = 2/3}$

$\sf{Here, 0.6 = 2/3}$