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Choose the simplest fraction for $0.5 4 ¯$ from the given options below.

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4790

4990

5290

None of these

answer is B.

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Detailed Solution

Given is the number

0.5 4 ¯

.
To express it in the form of

p q

, assume this number as, say x, and write in the expanded form as follows,

x = 0 ⋅ 544444.......

………... (i)
First, we shift 5 towards the left of the decimal, by multiplying each side of equation (1) by 10 as follows,

10 x = 5 ⋅ 44444.....

…………. (ii)
To shift the decimal point by one more place to the right, multiply the equation (ii) by 100 on each side as follows,

100 x = 54 ⋅ 44444.....

…………(iii)
Now, subtract equation (ii) from (iii) and simplify as follows,

100 x − 10 x = 54.44444..... − 5.44444..... 90 x = 49 x = 4990

From the above result, we can conclude that,

0.5 4 ¯ = 4990

.
So, it is the required rational form.
Hence, the correct option is (2).

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