A tape dispenser holds 1.14×104

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

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

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

14.478×104 mm2

Answer 1

To find the total area of the 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, perform the multiplication:

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

Calculating it step-by-step:

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

2. Now, multiply by the power of ten: \[ 14.478 \times 10^4 \]

To express this in proper scientific notation, you need to move the decimal point one place to the left, which means you will increase the exponent by 1:

\[ 14.478 \times 10^4 = 1.4478 \times 10^5 \]

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

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