Question

a tape dispenser holds milligrams of tape that has 12.7 m wide. Multiply the two numbers to find the total area and square millimeters of tape 1.14×10 to the fourth power write the product and scientific notation.

Answer 1

To find the total area of tape in square millimeters, you will multiply the tape length (in milligrams, which we assume is an indication of length here) by the width of the tape.

Let's clarify the problem properly. It seems you're using 1.14 × 10^4 milligrams (which we'll treat as millimeters of length for the sake of this calculation) and a width of 12.7 mm.

Here's the calculation:

1. **Length of tape**: 1.14 × 10^4 mm (which is the same as 11,400 mm)
2. **Width of tape**: 12.7 mm

Now, calculate the area:

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

Multiplying the numbers gives:

\[
1.14 \times 12.7 = 14.478
\]

Now, multiplying the powers of ten gives:

\[
10^4 \, \text{mm} \times 1 = 10^4 \, \text{mm}
\]

Combine the results:

\[
\text{Area} = 14.478 \times 10^4 \, \text{mm}^2
\]

Now, convert \(14.478\) into scientific notation:

\[
14.478 = 1.4478 \times 10^1
\]

So the area becomes:

\[
\text{Area} = (1.4478 \times 10^1) \times (10^4) = 1.4478 \times 10^{5} \, \text{mm}^2
\]

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

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