Use scientific notation to find the product of 7.13 × 10^-3 and 40. Include all of your calculations in your final answer.

Answer 1

To find the product of \( 7.13 \times 10^{-3} \) and \( 40 \), we can follow these steps:

1. Multiply the coefficients: The coefficients are \( 7.13 \) and \( 40 \). \[ 7.13 \times 40 = 285.2 \]

2. Combine with the power of ten: Since \( 7.13 \times 10^{-3} \) includes \( 10^{-3} \), we have: \[ 285.2 \times 10^{-3} \]

3. Convert to scientific notation: To convert \( 285.2 \) to scientific notation, we write it as \( 2.852 \times 10^2 \) (since we move the decimal point two places to the left).

4. Combine the powers of ten: Now we can rewrite our previous product: \[ 285.2 \times 10^{-3} = 2.852 \times 10^2 \times 10^{-3} \] When multiplying powers of ten, we add the exponents: \[ 10^{2 + (-3)} = 10^{-1} \]

5. Final result: Therefore, combining everything, we get: \[ 2.852 \times 10^{-1} \]

Thus, the final answer in scientific notation is: \[ \boxed{2.852 \times 10^{-1}} \]

Answer 2

can you make it a little less advanced and without all the symbols and slashes

Answer 3

Sure! Let's break it down step by step without using too many symbols.

1. Start by multiplying the numbers: We have 7.13 and 40.

   • When you multiply 7.13 by 40, you get 285.2.

2. Attach the power of ten: Since we started with 7.13 times 10 to the power of -3, we now need to deal with that.

   • So, we write it as 285.2 times 10 to the power of -3.

3. Convert 285.2 into scientific notation: We need to express 285.2 in scientific notation.

   • In scientific notation, 285.2 is written as 2.852 times 10 to the power of 2. (We move the decimal point two places to the left).

4. Combine the powers of ten: Now, we have 2.852 times 10 to the power of 2 and we still have our original 10 to the power of -3.

   • You add the exponents when combining powers of ten. So, 2 plus -3 gives us -1.

5. Final answer: Putting this all together, we get:

   • 2.852 times 10 to the power of -1.

So, the final answer in scientific notation is 2.852 times 10 to the power of -1.