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The number $4. 17 ¯$ expressed as a fraction is

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\frac{407}{99}

\frac{407}{100}

\frac{417}{100}

\frac{413}{99}

answer is D.

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Detailed Solution

We are given the recurring decimal

4. 17 ¯

.
To express this decimal as a fraction, assume this number as x and rewrite the decimal in expanded form as follows,

x = 4.17171717

……………. (i)
Since the repeating part of the decimal has two digits so, let us multiply each side of the equation (i) by 100, as follows,

100 x = 417.17171717

……………. (ii)
Now, we subtract equation (i) from (ii).

100 x − x = 417.171717..... − 4.171717.... 99 x = 413 x = 41399

So, from the above result, we can conclude that,

4. 17 ¯ = 41399

.
Hence, the correct option is (4).

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