229k views
1 vote
Using algebra, show that 1.381 (the 81 is recurring) subtract 0.81 ( the 81 is recurring) equals to 31/55

User Ajay Soman
by
7.3k points

1 Answer

1 vote

it is true that 81 as recurring decimal equals to 3/55

How to show that 81 as recurring decimal equals to 3/55

From the question, we have the following parameters that can be used in our computation:

1.381818181.....

This can be expressed as

1.3 + 0.081 + 0.00081 + 0.0000081

From the above, we have

First term, a = 0.081

Common ratio, r = 0.01

The sum to infinity on a geometric sequence is

S = a/(1 - r)

So, we have

S = 0.081/(1 - 0.01)

S = 0.081/(0.99)

Evaluate

S = 81/990

Simplify

S = 9/110

This gives

S = 3/55

Hence, 81 as recurring decimal equals to 3/55

Question

Using algebra, show that the 81 in 1.381818181..... equals to 3/55

User IronMan
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories