Simplify (0 . \overline{1})^{2}\{1-9(0.1 \overline{6})^{2}\}

NIFT PG 2019 Question Paper with solutions

Question : 23 of 150

Marks: +1, -0

Simplify

(0 . \ov{1})^{2}\{1-9(0.1 \ov{6})^{2}\}

Solution:

(\;{1}/{9})^{2}\{1-9(\;{16-1}/{90})^{2}\}

(converting decimal into fractions)

=\;{1}/{81}\{1-\;{9 × 15 × 15}/{90 × 90}\}=\;{1}/{81} ×\{1-\;{1}/{4}\}

=\;{1}/{81} × \;{3}/{4}=\;{1}/{108}

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