A tape dispenser holds 1.14×10^4

Question

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)
Responses

1.4478×105 mm2
1.4478 times 10 superscript 5 baseline mm squared

14.478×104 mm2
14.478 times 10 superscript 4 baseline mm squared

1.4478×104 mm2
1.4478 times 10 superscript 4 baseline mm squared

14.478×105 mm2
14.478 times 10 superscript 5 baseline mm squared
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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:

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

First, calculate \(1.14 \times 12.7\):

\[ 1.14 \times 12.7 = 14.478 \]

Now, since \(1.14\) is in scientific notation with \(10^4\), we have:

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

Next, convert \(14.478 \times 10^4\) into proper scientific notation. To do that, you want the coefficient to be between 1 and 10.

You can write \(14.478\) as \(1.4478 \times 10^1\), leading to:

\[ 14.478 \times 10^4 = 1.4478 \times 10^1 \times 10^4 = 1.4478 \times 10^{5} \]

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

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