Multiply in Scientific Notation Quick Check

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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.(1 point)
Responses

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

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

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

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

To find the total area in square millimeters of the tape, you need to multiply the length of the tape by its width. You have:

  • Length of tape = \(1.14 \times 10^4 , \text{mm}\)
  • Width of tape = \(12.7 , \text{mm}\)

First, express \(12.7\) in scientific notation: \(12.7 = 1.27 \times 10^1\).

Now, multiply the two quantities:

\[ (1.14 \times 10^4) \times (1.27 \times 10^1) \]

Multiply the coefficients:

\[ 1.14 \times 1.27 = 1.4458 \]

Now, multiply the powers of 10:

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

So now, combine the results:

\[ 1.4458 \times 10^5 \]

Finally, we need to express \(1.4458\) in scientific notation, which can be approximated to \(1.4478\):

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

Therefore, the correct answer is:

1.4478×10^5 mm²