Question

express 0.999 in the form p/ q​

Answer 1

Correct Question :

• express 0.9 bar in the form p/ q

To find :

• The p/ q form of 0.9 bar

Given :

• Rational number 0.9 bar

Solution :

Let us take $\sf\:0.\bar{9}$ as 'x'

So, x = $\sf\:0.\bar{9}$

• 10x = 10 × $\sf\:0.\bar{9}$
• 10x = $\sf\:9.999$
• 10x = 9 + x
• 10x - x = 9
• 9x = 9
• x = $\sf\dfrac{9}{9}$ or $\sf\dfrac{1}{1}$

Required explanation :

When a digit after decimal repeats then we use the bar symbol to represent it .

For example if in the rational number 0.877777777 the number 7 repeats we would write it like $\sf\:0.8\bar{7}$ and if the number is 0.666666 then it will be written as $\sf\:0.\bar{6}$