Question
A tape dispenser holds 1.14 x 10^4 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.
answers:
1.4478 x 10^5 mm^2
14.478 x 10^5 mm^2
1.4478 x 10^4 mm^2
14.478 x 10^4 mm^2
answers:
1.4478 x 10^5 mm^2
14.478 x 10^5 mm^2
1.4478 x 10^4 mm^2
14.478 x 10^4 mm^2
Answers
GPT-4o mini
To find the total area of the tape in square millimeters, 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, multiply these two values:
\[
\text{Area} = 1.14 \times 10^4 \text{ mm} \times 12.7 \text{ mm}
\]
First, calculate \(1.14 \times 12.7\):
\[
1.14 \times 12.7 = 14.478
\]
Next, we can combine this with the power of ten:
\[
\text{Area} = 14.478 \times 10^4 \text{ mm}^2
\]
Since scientific notation typically has a single non-zero digit to the left of the decimal, we should convert \(14.478\) to scientific notation:
\[
14.478 = 1.4478 \times 10^1
\]
So we adjust the area accordingly:
\[
\text{Area} = (1.4478 \times 10^1) \times 10^4 = 1.4478 \times 10^{5} \text{ mm}^2
\]
Therefore, the total area in scientific notation is:
\[
\boxed{1.4478 \times 10^5 \text{ mm}^2}
\]
Given:
- Length of tape = \(1.14 \times 10^4\) mm
- Width of tape = 12.7 mm
Now, multiply these two values:
\[
\text{Area} = 1.14 \times 10^4 \text{ mm} \times 12.7 \text{ mm}
\]
First, calculate \(1.14 \times 12.7\):
\[
1.14 \times 12.7 = 14.478
\]
Next, we can combine this with the power of ten:
\[
\text{Area} = 14.478 \times 10^4 \text{ mm}^2
\]
Since scientific notation typically has a single non-zero digit to the left of the decimal, we should convert \(14.478\) to scientific notation:
\[
14.478 = 1.4478 \times 10^1
\]
So we adjust the area accordingly:
\[
\text{Area} = (1.4478 \times 10^1) \times 10^4 = 1.4478 \times 10^{5} \text{ mm}^2
\]
Therefore, the total area in scientific notation is:
\[
\boxed{1.4478 \times 10^5 \text{ mm}^2}
\]
are you sure
GPT-4o mini
Let’s verify the calculation step-by-step to ensure accuracy:
1. **Length of tape:** \( 1.14 \times 10^4 \) mm
2. **Width of tape:** \( 12.7 \) mm
Now, we multiply these two values to find the area:
\[
\text{Area} = \text{Length} \times \text{Width} = (1.14 \times 10^4) \times 12.7
\]
3. **Calculate \( 1.14 \times 12.7 \):**
\[
1.14 \times 12.7 = 14.478
\]
4. **Combine with the scientific notation for length:**
The length is in scientific notation, so:
\[
\text{Area} = 14.478 \times 10^4 \text{ mm}^2
\]
5. **Convert \( 14.478 \) into scientific notation:**
To convert \( 14.478 \) into scientific notation, we express it as:
\[
14.478 = 1.4478 \times 10^1
\]
6. **Combine it with \( 10^4 \):**
\[
\text{Area} = (1.4478 \times 10^1) \times 10^4 = 1.4478 \times 10^{5} \text{ mm}^2
\]
The calculation and conversion were executed correctly, confirming that the total area of tape is:
\[
\boxed{1.4478 \times 10^5 \text{ mm}^2}
\]
So, yes, the answer is indeed accurate. Thank you for prompting this verification!
1. **Length of tape:** \( 1.14 \times 10^4 \) mm
2. **Width of tape:** \( 12.7 \) mm
Now, we multiply these two values to find the area:
\[
\text{Area} = \text{Length} \times \text{Width} = (1.14 \times 10^4) \times 12.7
\]
3. **Calculate \( 1.14 \times 12.7 \):**
\[
1.14 \times 12.7 = 14.478
\]
4. **Combine with the scientific notation for length:**
The length is in scientific notation, so:
\[
\text{Area} = 14.478 \times 10^4 \text{ mm}^2
\]
5. **Convert \( 14.478 \) into scientific notation:**
To convert \( 14.478 \) into scientific notation, we express it as:
\[
14.478 = 1.4478 \times 10^1
\]
6. **Combine it with \( 10^4 \):**
\[
\text{Area} = (1.4478 \times 10^1) \times 10^4 = 1.4478 \times 10^{5} \text{ mm}^2
\]
The calculation and conversion were executed correctly, confirming that the total area of tape is:
\[
\boxed{1.4478 \times 10^5 \text{ mm}^2}
\]
So, yes, the answer is indeed accurate. Thank you for prompting this verification!