Question

What is 1.7¯(repeating) expressed as a fraction in simplest form?

Answer 1

LET X=1.777
10*1.777(BECAUSE ONLY ONE DIGIT REPEATS)
=17.777
17.777-1.777=10X-X
16=9X
X=16/9

THEREFORE THE FRACTION IS 16/9

Answer 2

Let x = 1.7⁻ (bar)

∴ x = 1.777                                  ............(i)

We have to find, the fraction in simplest form of 1.7⁻(bar).

Solution:

Multiplying equation (i) by 10 in both sides, we get

10x = 10(1.777)                            

⇒ 10x = 17.777                              ............(ii)

On subtracting (i) from (ii), we get

10x - x = 17.777 - 1.777    

⇒ 9x = 16

Dividing both sides by 9, we get

⇒ $\dfrac{9x}{9}$ = $\dfrac{16}{9}$

⇒ x = $\dfrac{16}{9}$

⇒ x = $\dfrac{9+7}{9}$

⇒ x = $\dfrac{9}{9}+\dfrac{7}{9}$

⇒ x = $1+\dfrac{7}{9}$

⇒ x = $1\dfrac{7}{9}$

∴ The fraction in simplest form of 1.7⁻(bar) = $\dfrac{16}{9}$ or, $1\dfrac{7}{9}$