Maths-
General
Easy

Question

Express 23.324242424….. in p/q form, where p and q are integers

hintHint:

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: 23.324242424


    The given number is  23.324242424….. which can be written as 23.324
    Let’s say X=23.324
    Step 1 of 3:
    x=23.324
    Multiplying both sides by 10
    10x=233.24  ………..(1)
    Step 2 of 3:
    Now multiply both sides of equation (1) by 100
    1000x=23324.24................(2)
    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 23324.24 minus 23.324 end cell row cell 990 x equals 23324.24 minus 233.24 end cell row cell 990 x equals 23091 end cell row cell x equals 23091 over 990 end cell end table
    Final Answer:
    Hence, the p/q form of 23.324242424….. is 23091 over 990
    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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