Simplify:\(100 \times \frac{{{{0.51}^2} + {{0.05}^2} + {{0.023}^2}}}{{{{0.051}^2} + {{0.005}^2} + {{0.0023}^2}}}\)
Solution
Correct Answer: Option E
Given expression:
\(100{\rm{\;}} \times \frac{{{{0.51}^2} + {{0.05}^2} + {{0.023}^2}}}{{{{0.051}^2} + {{0.005}^2} + {{0.0023}^2}}}\)
Let 0.51 = a, 0.05 = b, 0.023 = c
Then the given expression becomes
\(100{\rm{\;}} \times \frac{{{a^2} + {b^2} + {c^2}}}{{{{\left( {0.1 \times a} \right)}^2} + {{\left( {0.1 \times b} \right)}^2} + {{\left( {0.1 \times c} \right)}^2}}}\)\(\Rightarrow \frac{{100}}{{0.01}}{\rm{\;}} \times \frac{{{a^2} + {b^2} + {c^2}}}{{{{\left( a \right)}^2} + {{\left( b \right)}^2} + {{\left( c \right)}^2}}}\)
= 10000
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