Question

How do you convert $$1.7$$ (7 repeating) as a fraction?

Answer 1

Hint: To convert a decimal number containing a bar on a digit into a fraction, we shift its decimal to the right-hand side by multiplying the number by 10 and then subtract the original number from it and simplify it.

Complete step by step solution:
As per the question, we have $$1.7$$ (7 repeating), which means $1.77\bar{7}$ . The third digit has a bar, which means that 7 is repeating again and again.
We will consider given number $$x=1.77\bar{7}......(1)$$
We will multiply equation (1) by 10
$10\times x=10\times 1.77\bar{7}$
$10x=17.77\bar{7}......(2)$
Subtract equation (1) from equation (2)
$10x-x=17.77\bar{7}-1.77\bar{7}$
Simply above equation
$9x=16$
$x={\displaystyle \frac{16}{9}}$

Hence, ${\displaystyle \frac{16}{9}}$ is a fraction form of $1.77\bar{7}$

To convert it into mix fraction we divide 16 by 9
$x={\displaystyle \frac{16}{9}}\Rightarrow 1{\displaystyle \frac{7}{9}}$

And mix fraction is $1{\displaystyle \frac{7}{9}}$

Note:
We should remember that we need to remove the bar from the number. So, we shift decimal towards the right, by multiplication operation and then subtract both numbers, these steps will remove the bar from the number.