Maths-

General

Easy

Question

# Express the following recurring decimal as a vulgar fraction

1.3454545454545…………

## The correct answer is: 74/55

### Hint:

A repeating decimal is a decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely repeated portion is not zero. These repeating can be expressed in p/q form using some simple methods.

Solution

The given number is 1.3454545454545…… which can be written as

Let’s say X=

Multiplying both sides by 10

................(1)

Step 2 of 3:

Subtracting equation (2) by equation (1)

Simplifying the fraction:

Final Answer:

Hence, the p/q form of 1.3454545454545…… is .

Note: This question can also be solved by using the concept of the sum of infinite terms which are in geometric progression.

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