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Mathematics

The recurring decimal 0.45‾0.4\overline{5} when converted to a vulgar fraction is

  1. 45100\dfrac{45}{100}

  2. 4599\dfrac{45}{99}

  3. 4190\dfrac{41}{90}

  4. 4199\dfrac{41}{99}

Decimals

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Answer

Let x = 0.4555… (i)

Multiplying both sides by 10 (to move the decimal point past the non-repeating digit):

10x = 4.5555… (ii)

Multiplying both sides by 10 (to move the decimal point past the first repeating digit):

100x = 45.5555… (iii)

On subtracting (ii) from (iii), we get:

(100x - 10x) = (45.5555…) - (4.5555…)

90x = 41

x=4190x = \dfrac{41}{90}

Hence, option 3 is the correct option.

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