Final answer:
The expression evaluates to -51.5 after following the order of operations, which includes working out the parentheses, squaring the negative decimal, division, and then performing the subtraction and addition.
Step-by-step explanation:
To evaluate the expression -[4.2-3(2.1)]/(-0.2)²+1, we must carefully follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
First, calculate the expression inside the brackets:
- 3(2.1) = 6.3
- 4.2 - 6.3 = -2.1
So the expression becomes -(-2.1)/(-0.2)²+1.
Then, calculate the square of -0.2, which is -0.2 * -0.2 = 0.04.
The expression now reads -(-2.1)/0.04 + 1.
Divide -2.1 by 0.04, giving us 52.5. With the negative sign outside, it becomes -52.5.
Finally, add 1 to -52.5, resulting in -51.5.
The value of the expression is -51.5.