A tape dispenser holds 1.14×10^4 mm of tape that is 12.7 mm wide. Multiply the two numbers to find the total area in square millimeters of tape. Write the product in scientific notation.(1 point)

Question

Responses

1.4478×10^5 mm2
1.4478 times 10 superscript 5 baseline mm squared

14.478×10^5 mm2
14.478 times 10 superscript 5 baseline mm squared

1.4478×10^4 mm2
1.4478 times 10 superscript 4 baseline mm squared

14.478×10^4 mm2

Answer 1

To find the total area of tape in square millimeters, you 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, perform the multiplication:

\[ \text{Area} = \text{Length} \times \text{Width} = (1.14 \times 10^4 , \text{mm}) \times (12.7 , \text{mm}) \]

First, multiply the numerical parts:

\[ 1.14 \times 12.7 = 14.478 \]

Next, we keep the \(10^4\) part:

\[ \text{Area} = 14.478 \times 10^4 , \text{mm}^2 \]

Since \(14.478\) is not in standard scientific notation (which requires that the leading number is between \(1\) and \(10\)), we can convert it to \(1.4478 \times 10^1\):

\[ 14.478 \times 10^4 = 1.4478 \times 10^1 \times 10^4 = 1.4478 \times 10^{5} , \text{mm}^2 \]

Thus, the total area of the tape in scientific notation is:

\[ \boxed{1.4478 \times 10^5 , \text{mm}^2} \]