Question

Katelyn incorrectly simplified an expression using the steps shown below.

(3 x 10^-4) (9 x 10^2) + 0.0002 (27 x 10^-2) + 0.0002 (27 x 10^-2) + (2 x 10^-4) = (0.27 x 10^-4) + (2 x 10^-4) = 2.27 x 10^-8.

Answer 1

To correctly simplify the given expression, we need to follow the order of operations and perform the operations within parentheses first, then the multiplications.

Step-by-step explanation:

The student has incorrectly simplified the given expression. To correctly simplify the expression, we need to follow the order of operations and perform the operations within parentheses first, then the multiplications. Let's break it down:

1. (3 x 10-4) (9 x 102) = 27 x 10-2
2. 0.0002 (27 x 10-2) = 0.0002 x 27 x 10-2 = 0.0054 x 10-2 = 0.000054
3. 0.0002 (27 x 10-2) + 0.0002 (27 x 10-2) = 2 x 0.000054 = 0.000108
4. (0.27 x 10-4) + (2 x 10-4) = 0.27 x 10-4 + 2 x 10-4 = 2.27 x 10-4

Therefore, the correct simplification of the expression is 2.27 x 10-4.