Which of the following options is equal to \(((0.3 \times 0.3 + 0.01)(0.1 \times 0.1 + 0.09)^{-1})^2\)?
1. 0.1
2. 0.01
3. 0.09
4. 1
Answer (1)
To solve the expression (( 0.3 × 0.3 + 0.01 ) ( 0.1 × 0.1 + 0.09 ) − 1 ) 2 , we need to evaluate each part step-by-step.
Calculate the first part:
( 0.3 × 0.3 + 0.01 )
= 0.09 + 0.01 = 0.10
Calculate the second part:
( 0.1 × 0.1 + 0.09 )
= 0.01 + 0.09 = 0.10
Take the inverse of the second part:
( 0.10 ) − 1 = 0.10 1 = 10
Multiply the results from the first and third steps:
0.10 × 10 = 1
Square the result from step 4:
( 1 ) 2 = 1
Therefore, the value of the given expression is 1 .
So, the correct option is 4. 1 .
