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Maths-

General

Easy

Question

Express the following recurring decimal as a vulgar fraction
0.15151515………..

hint Hint:

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.

The correct answer is: 5/33

The given number is 0.15151515…… which can be written as
Let’s say $x equals 0. bottom enclose 15$
Step 1 of 2:
$x equals 0. bottom enclose 15$
Multiplying both sides by 100
$space space 100 x equals 15. bottom enclose 15 space space space space horizontal ellipsis horizontal ellipsis horizontal ellipsis.. left parenthesis 2 right parenthesis$
Step 2 of 2:
Subtracting equation (2) by equation (1)
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 100 x minus x equals 15.15 with _ below minus 0.15 end cell row cell 99 x equals 15 end cell row cell x equals 15 over 99 end cell end table$
Simplifying the fraction:
$x equals 5 over 33$
Final Answer:
Hence, the vulgar fraction or fraction of 0.15151515…… is . $5 over 33$

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