Question

A tape dispenser holds 1.14 x 10 to the fourth power 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.

Answer 1

To find the total area in square millimeters of the tape, we 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, we can multiply these two values together:

\[
\text{Total area} = (1.14 \times 10^4 \, \text{mm}) \times (12.7 \, \text{mm})
\]

First, perform the multiplication of the coefficients:

\[
1.14 \times 12.7 = 14.478
\]

Next, we consider the powers of ten. Since 12.7 has no power of ten, we can just maintain the \( 10^4 \):

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

Now, we need to express \( 14.478 \) in scientific notation. We can do this by moving the decimal point one place to the left, which gives us:

\[
1.4478 \times 10^1
\]

Now, we can combine the powers of ten:

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

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

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