Question

Kendra finds the dimensions of a sticky note. she uses a meter stick to determine that the dimensions are 1.25 time 10^negative 8 meters wide by 2.5 times 10^negative 6 meters long. use scientific notation to write the dimensions in millimeters.

note: 1 meter is equal to 1,000 millimeters

Answer 1

To convert the dimensions of the sticky note from meters to millimeters, we'll multiply each dimension by \(1,000\) (or \(10^3\)) since \(1 \text{ meter} = 1,000 \text{ millimeters}\).

1. **Width:**
\[
1.25 \times 10^{-8} \text{ meters} \times 1,000 = 1.25 \times 10^{-8} \times 10^3 = 1.25 \times 10^{-5} \text{ meters}
\]

2. **Length:**
\[
2.5 \times 10^{-6} \text{ meters} \times 1,000 = 2.5 \times 10^{-6} \times 10^3 = 2.5 \times 10^{-3} \text{ meters}
\]

Now we can rewrite both dimensions in millimeters in scientific notation:

- Width: \(1.25 \times 10^{-5} \text{ m} = 1.25 \times 10^{-5} \times 10^3 \text{ mm} = 1.25 \times 10^{-2} \text{ mm}\)
- Length: \(2.5 \times 10^{-3} \text{ m} = 2.5 \times 10^{-3} \times 10^3 \text{ mm} = 2.5 \text{ mm}\)

So, the dimensions of the sticky note in millimeters in scientific notation are:

- Width: \(1.25 \times 10^{-2} \text{ mm}\)
- Length: \(2.5 \text{ mm}\)

These can also be expressed as follows for clarity:
- Width: \(0.0125 \text{ mm}\) (or \(1.25 \times 10^{-2} \text{ mm}\))
- Length: \(2.5 \text{ mm}\) (or \(2.5 \times 10^{0} \text{ mm}\))