To find the total area of the tape, you can multiply the length of the tape by the width of the tape.
Given:
- Length of tape = \( 1.14 \times 10^4 \) mm
- Width of tape = \( 12.7 \) mm
Let's perform the multiplication:
\[ \text{Area} = \text{Length} \times \text{Width} = (1.14 \times 10^4) \times 12.7 \]
First, multiply the coefficients:
\[ 1.14 \times 12.7 = 14.458 \]
Next, since \( 1.14 \) has two decimal places and \( 12.7 \) has one decimal place, we must adjust the decimal point when converting it to scientific notation. The final multiplication will adjust for the exponent of the powers of ten.
Now, we combine that with \( 10^4 \):
\[ \text{Area} = 14.458 \times 10^4 \]
Next, convert \( 14.458 \) into scientific notation. \( 14.458 \) can be expressed as \( 1.4458 \times 10^1 \):
\[ \text{Area} = 1.4458 \times 10^1 \times 10^4 = 1.4458 \times 10^{1 + 4} = 1.4458 \times 10^5 \]
So the total area of the tape in square millimeters, expressed in scientific notation, is:
\[ \boxed{1.4458 \times 10^5} \text{ mm}^2 \]