Question

A tape dispenser holds 1.14×104 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.
Responses

1.4478×105 mm2
1.4478×105 mm2
- no response given

1.4478×104 mm2
1.4478×104 mm2
- no response given

14.478×104 mm2
14.478×104 mm2
- no response given

14.478×105 mm2

Answer 1

To find the total area of tape in square millimeters, you need to 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 we can perform the multiplication:

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

Calculating the product:

1. First, multiply the coefficients:
\[
1.14 \times 12.7 = 14.478
\]

2. Next, combine this with the power of ten:
\[
\text{Area} = 14.478 \times 10^4 \text{ mm}^2
\]

3. Since \( 14.478 \times 10^4 \) is not in proper scientific notation (it should only have one non-zero digit to the left of the decimal), we convert it to:
\[
1.4478 \times 10^5 \text{ mm}^2
\]

Thus, the total area of the tape in scientific notation is \( \mathbf{1.4478 \times 10^5 \text{ mm}^2} \).

From the given responses, the correct answer is:

**1.4478×105 mm²**