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.

Answer 1

To find the total area of the tape, we can 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, let's multiply these two values:

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

First, we multiply the coefficients (1.14 and 12.7):

\[
1.14 \times 12.7 = 14.478
\]

Next, we multiply the powers of 10:

\[
10^4
\]

Now combine these results:

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

To express this in scientific notation, we need to adjust \( 14.478 \) so that it’s between 1 and 10. We can do that by moving the decimal place one place to the left, which will increase the exponent by 1:

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

Thus, we rewrite the area:

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

So, the total area of the tape in scientific notation is:

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