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Surds

If 1.666666 …...

Question

If 1.666666...... is a rational number and can be expressed in $\frac{p}{q}$ form, then find p + q.

A

5

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B

6

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C

7

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D

8

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Solution

The correct option is D
8

Let 'x' = 1.6666...then 10x = 16.666666,
10x = 15 + x,
9x = 15
Hence x = $\frac{5}{3}$
So, p + q = 8

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