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.

Question

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

Answer 1

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: $$\boxed{{\displaystyle 1.4478\times {10}^5{\text{ mm}}^2}}$$

Answer 2

are you sure

Answer 3

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:

$$\boxed{{\displaystyle 1.4478\times {10}^5{\text{ mm}}^2}}$$

So, yes, the answer is indeed accurate. Thank you for prompting this verification!