3.2x10^4 1.95x10^6 8.03x10^-8 2.56x10^-2 4.82x10^12

Question

choose 2 of the scientific numbers form the list and add them. show your work.

Answer 1

To add two numbers in scientific notation, they need to be expressed with the same exponent. Let's choose \( 1.95 \times 10^6 \) and \( 4.82 \times 10^{12} \) from your list.

Step 1: Convert the numbers to have the same exponent.

We will convert \( 1.95 \times 10^6 \) to the same exponent as \( 4.82 \times 10^{12} \). To do this, we can write:

\[ 1.95 \times 10^6 = 1.95 \times 10^6 \times \frac{10^{6}}{10^{6}} = 1.95 \times 10^{12} \times 10^{-6} = 0.00000195 \times 10^{12} \]

This isn't helping with the mathematics, so let's just move \( 4.82 \) down and adjust \( 1.95 \):

\[ 1.95 \times 10^6 = 0.00000195 \times 10^{12} \]

Step 2: Add the numbers.

Now we can add the two values: \[ 4.82 \times 10^{12} + 0.00000195 \times 10^{12} = (4.82 + 0.00000195) \times 10^{12} \]

Calculating \( 4.82 + 0.00000195 \): \[ 4.82 + 0.00000195 = 4.82000195 \]

Step 3: Write the final answer in scientific notation.

Thus we have: \[ 4.82000195 \times 10^{12} \]

To express this in proper scientific notation, we can round it to a suitable number of significant figures. Rounding to two decimal places (as in \(4.82\)) gives:

\[ 4.82 \times 10^{12} \]

Now, if more precision is required we can keep it as \(4.82000195\), but typically for scientific notation, we simplify to \(4.82 \times 10^{12}\) based on precision needed.

Final answer: \[ \mathbf{4.82 \times 10^{12}} \]

Answer 2

choose two scientific numbers from the list and subtract them. show your work.

Answer 3

Let's choose \( 4.82 \times 10^{12} \) and \( 2.56 \times 10^{-2} \) from your list to perform the subtraction.

Step 1: Convert the numbers to have the same exponent.

We can express \( 4.82 \times 10^{12} \) in terms of \( 10^{-2} \) for easier subtraction:

\[ 4.82 \times 10^{12} = 4.82 \times 10^{12} \times \frac{10^{-2}}{10^{-2}} = 4.82 \times 10^{12} \times 10^{-2} \times 10^{2} = 4.82 \times 10^{10} \times 10^{2} = 4.82 \times 100 \times 10^{10} \]

Calculating: \[ 4.82 \times 10^{12} = 4.82 \times 100 \times 10^{10} = 482000000000 \text{ (but we actually won't use the full value)} \]

Now, we can express \( 2.56 \times 10^{-2} \):

Step 2: Convert \( 4.82 \times 10^{12} \) back to have an exponent of \( 10^{-2} \): \[ 4.82 \times 10^{12} = 482000000000 \times 10^{-2} = 4820000000 \times 10^{10} \] (Here we can note we haven't fully simplified so we will adjust).

Step 3: Adjust \( 4.82 \times 10^{12} \) based on other calculations: To properly calculate, I can keep \( 2.56 \times 10^{-2} \) as it is.

So we have: \[ 4.82 \times 10^{12} \text{ (this is greatly larger than the other number)} \]

Now let's express \( 2.56 \times 10^{-2} \) in terms of \( 10^{12}\): \[ 2.56 \times 10^{-2} = 0.0000256 \times 10^{12} \]

Step 4: Now perform the subtraction:

Rewrite \( 4.82 \times 10^{12} \) for easy calculation: \[ 4.82 \times 10^{12} - 0.0000256 \times 10^{12} = (4.82 - 0.0000256) \times 10^{12} \]

Now calculating: \[ 4.82 - 0.0000256 = 4.8199744 \]

Step 5: Write the final answer in scientific notation.

Thus we have: \[ 4.8199744 \times 10^{12} \]

In scientific notation, we can round appropriately depending on precision; rounding to two decimal places gives: \[ 4.82 \times 10^{12} \]

However, if we want to maintain higher precision (more significant figures), we can keep: \[ 4.8199744 \times 10^{12} \]

Final answer: \[ \mathbf{4.82 \times 10^{12}} \text{ or } \mathbf{4.8199744 \times 10^{12}} \] (based on how you want to express precision).