To find the total area of the tape in square millimeters, we can multiply the length of the tape by its width.
Given:
- Length of tape = \( 1.14 \times 10^4 \) mm
- Width of tape = \( 12.7 \) mm
We can do the multiplication as follows:
\[ \text{Area} = \text{Length} \times \text{Width} = (1.14 \times 10^4 , \text{mm}) \times (12.7 , \text{mm}) \]
First, we multiply the numerical parts:
\[ 1.14 \times 12.7 = 14.478 \]
Next, we handle the powers of ten:
\[ 10^4 \text{ (from length)} \]
Thus, the area in mm² before converting to scientific notation is:
\[ \text{Area} = 14.478 \times 10^4 , \text{mm}^2 \]
Now, we need to convert \( 14.478 \) into scientific notation. It is equivalent to:
\[ 1.4478 \times 10^1 \]
Now let's combine:
\[ \text{Area} = 1.4478 \times 10^1 \times 10^4 = 1.4478 \times 10^{5} , \text{mm}^2 \]
So, the total area of the tape in square millimeters, written in scientific notation, is:
\[ \boxed{1.4478 \times 10^5 , \text{mm}^2} \]
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