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A day full of math games & activities. Find one near you.

Show that 0.142857142857... = 1/7

Solution:

Given, 0.142857142857... = 1/7

We have to prove the above expression.

Considering LHS,

LHS: 0.142857142857...

Let x = 0.142857142857... ------------------ (1)

Multiplying by 1000000 on both sides,

1000000x = 1000000(0.142857142857... )

1000000x = 142857.142857 ----------------- (2)

Subtracting (1) and (2),

1000000x - x = 142857.142857 - 0.142857142857

999999x = 142857

x = 142857/999999

x = 1/7

= RHS

LHS = RHS

Hence proved.

✦ Try This: Show that 0.505050... = 50/99

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1

NCERT Exemplar Class 9 Maths Exercise 1.3 Problem 8

Show that 0.142857142857... = 1/7

Summary:

0.142857142857… is a non terminating and recurring decimal so it is a rational number. It is proven that 0.142857142857... = 1/7

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