When multiplying two numbers in scientific notation, what operations do you use on the coefficients and the exponents of the powers of 10?(1 point)

Question

Responses

Add the coefficients and add the exponents of the powers of 10.
Add the coefficients and add the exponents of the powers of 10.

Add the coefficients and multiply the exponents of the powers of 10.
Add the coefficients and multiply the exponents of the powers of 10.

Multiply the coefficients and add the exponents of the powers of 10.
Multiply the coefficients and add the exponents of the powers of 10.

Multiply the coefficients and multiply the exponents of the powers of 10.

Answer 1

When multiplying two numbers in scientific notation, you should:

Multiply the coefficients and add the exponents of the powers of 10.

So, out of the options given, the correct response is:

Multiply the coefficients and add the exponents of the powers of 10.

Answer 2

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 3

To find the total area of the tape in square millimeters, we will multiply the length of the tape (in mm) by its width (in mm).

Given:

• Length of tape: \(1.14 \times 10^4\) mm
• Width of tape: \(12.7\) mm

Step 1: Multiply the coefficients

First, multiply the coefficients:

\[ 1.14 \times 12.7 = 14.478 \]

Step 2: Add the exponents

Next, we can add the exponents of \(10\):

• The exponent of the first number is \(10^4\).
• The width has no exponent, which can be considered as \(10^0\).

Adding the exponents:

\[ 4 + 0 = 4 \]

Step 3: Combine the results

Now, combine the results to form the scientific notation. Since \(14.478\) is not between \(1\) and \(10\), we need to adjust it:

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

So, the product in scientific notation is:

\[ 1.4478 \times 10^1 \times 10^4 = 1.4478 \times 10^{5} \]

Final Answer

Therefore, the total area in square millimeters of tape is:

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

Answer 4

A sugar cube has a volume of about 4.9 ml. What is the total volume in milliliters of 1.5×106 sugar cubes?

Answer 5

To find the total volume of \(1.5 \times 10^6\) sugar cubes, each with a volume of \(4.9\) ml, you will multiply the number of cubes by the volume of one sugar cube.

Step 1: Multiply the numbers

We need to multiply \(1.5 \times 10^6\) by \(4.9\).

Step 1.1: Multiply the coefficients

First, multiply the coefficients:

\[ 1.5 \times 4.9 = 7.35 \]

Step 1.2: Add the exponents

Next, since \(4.9\) can be considered as \(4.9 \times 10^0\), we add the exponents:

\[ 6 + 0 = 6 \]

Step 2: Combine the results

Now combine the results:

\[ 7.35 \times 10^6 \]

Step 3: Write in scientific notation

The total volume in milliliters of \(1.5 \times 10^6\) sugar cubes is:

\[ \boxed{7.35 \times 10^6} \text{ ml} \]

Answer 6

Multiply 0.75 by 2.8×10−5 .

Answer 7

To multiply \(0.75\) by \(2.8 \times 10^{-5}\), follow these steps:

Step 1: Multiply the coefficients

First, multiply the coefficients:

\[ 0.75 \times 2.8 = 2.1 \]

Step 2: Keep the power of 10

Since \(2.8 \times 10^{-5}\) has a power of \(10^{-5}\), we keep that as is:

\[ 2.1 \times 10^{-5} \]

Final Result

Thus, the result of multiplying \(0.75\) by \(2.8 \times 10^{-5}\) is:

\[ \boxed{2.1 \times 10^{-5}} \]