Multiply in Scientific Notation Quick Check

Question

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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

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

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

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

1.4478×104 mm2

Answer 1

To find the total area in square millimeters of tape, you need to multiply the length of the tape (in mm) by the width of the tape (also in mm):

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:

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

When multiplying in scientific notation, you multiply the coefficients and add the exponents:

1. Multiply the coefficients: \[ 1.14 \times 1.27 = 1.4438 \]

2. Add the exponents: \[ 10^4 \times 10^1 = 10^{4+1} = 10^5 \]

So, the product becomes: \[ 1.4438 \times 10^5 \]

Lastly, rounding \(1.4438\) to four significant figures gives \(1.4478\).

Thus, the final answer in scientific notation is: \[ \boxed{1.4478 \times 10^5 , \text{mm}^2} \]

So the correct response is: 1.4478×10^5 mm²