Question

In this problem, you will practice added, subtracting, multiplying, and dividing numbers written in scientific notation. For each part, use the following numbers.

3.2 x 10^4, 1.95 x 10^6, 8.03 x 10^-8, 2.56 x 10^-2, 4.82 x 10^12
Choose two scientific numbers from the list and add them. Show your work.

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's choose 3.2 x 10^4 and 1.95 x 10^6.

To add these two numbers, we need to ensure that they have the same exponent. In this case, we can convert 3.2 x 10^4 to 3.2 x 10^6 to have the same exponent as 1.95 x 10^6.

So, 3.2 x 10^6 + 1.95 x 10^6 = (3.2 + 1.95) x 10^6 = 5.15 x 10^6.

Therefore, the sum of 3.2 x 10^4 and 1.95 x 10^6 is 5.15 x 10^6.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To add two numbers written in scientific notation, you need to make sure the exponents (powers of 10) are the same. Let's choose two numbers from the list and add them.

Let's choose 3.2 x 10^4 and 1.95 x 10^6.

To add them, we need to make the exponents the same.

Step 1: Adjust the exponent to make them the same.
Since 10^4 is smaller than 10^6, we need to adjust the first number by multiplying it by 10^2 to increase the exponent to 6.

(3.2 x 10^4) x (10^2) = 3.2 x 10^6

Now that the exponents are the same, we can add the two numbers.

Step 2: Add the numbers.
3.2 x 10^6 + 1.95 x 10^6 = (3.2 + 1.95) x 10^6

Step 3: Simplify the addition result.
3.2 + 1.95 = 5.15

So, the sum of 3.2 x 10^4 and 1.95 x 10^6 is 5.15 x 10^6.

Answer 3

[AI-generated answer — Explain Bot]

To add two numbers written in scientific notation, we need to make sure that the exponents (powers of 10) are the same. Here's the step-by-step process to add two scientific numbers:

Step 1: Choose two numbers from the list:
Let's select 3.2 x 10^4 and 1.95 x 10^6.

Step 2: Match the exponents:
To add numbers, we need to make sure the exponents (powers of 10) are the same. In this case, we have 10^4 and 10^6. In order to proceed, we must make the exponents equal.
We can do this by moving the decimal point of the number with the smaller exponent to the right until its exponent matches the greater one. Each move to the right increases the exponent by 1.

Step 3: Adjusting the decimal point:
For 3.2 x 10^4, we will move the decimal point two places to the right, and this will change the number to 32,000.
So, 3.2 x 10^4 becomes 32,000.

Step 4: Add the adjusted numbers:
Now that the exponents are the same (10^6), we can add the two numbers:
32,000 + 1,950,000 = 1,982,000

Step 5: Expressing the result in scientific notation:
To write the result in scientific notation, we find the correct position of the decimal point. Since we moved the decimal point two places to the right in the first number, we need to move it back two places in the final result.
So, our final answer is 1.982 x 10^6.

Thus, when we add 3.2 x 10^4 and 1.95 x 10^6, the result is 1.982 x 10^6.