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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 $1.3 bottom enclose 45$
Let’s say X= $1.3 bottom enclose 45$
Multiplying both sides by 10
$10 x equals 1.3 bottom enclose 45$ ................(1)
Step 2 of 3:
Subtracting equation (2) by equation (1)
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 1000 x minus 10 x equals 1345.45 with _ below minus 13.45 with _ below end cell row cell 990 x equals 1332 end cell row cell x equals 1332 over 990 end cell end table$
Simplifying the fraction:
Final Answer:
Hence, the p/q form of 1.3454545454545…… is . $74 over 55$
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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