To find the total area of the tape, 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
Now, let's multiply these two values:
\[ \text{Area} = \text{Length} \times \text{Width} = (1.14 \times 10^4 , \text{mm}) \times (12.7 , \text{mm}) \]
First, we multiply the coefficients (1.14 and 12.7):
\[ 1.14 \times 12.7 = 14.478 \]
Next, we multiply the powers of 10:
\[ 10^4 \]
Now combine these results:
\[ \text{Area} = 14.478 \times 10^4 , \text{mm}^2 \]
To express this in scientific notation, we need to adjust \( 14.478 \) so that it’s between 1 and 10. We can do that by moving the decimal place one place to the left, which will increase the exponent by 1:
\[ 14.478 = 1.4478 \times 10^1 \]
Thus, we rewrite the area:
\[ \text{Area} = (1.4478 \times 10^1) \times 10^4 = 1.4478 \times 10^{5} , \text{mm}^2 \]
So, the total area of the tape in scientific notation is:
\[ \boxed{1.4478 \times 10^5} , \text{mm}^2 \]
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