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

Question

3.2 × 10^4 | 1.95 × 10^6 | 8.03 × 10^-8 | 2.56 × 10^-2 | 4.82 × 10^12
a. Choose two of the scientific numbers from the list and add them. Show your work.
b. Choose two of the scientific numbers from the list and subtract them. Show your work. Make it not too long and make it understandable none of that “ 3.2 \times 10^4 = 3.2 \times 10^4 \times \frac{100}{100} = 3.2 \times 10^4 \times 10^2 = 3.2 \times 10^6 \times 10^{-2}
\]
This can be rewritten as:” bs

Answer 1

Sure! Let's go through the operations step by step.

a. Addition

Let's add \( 3.2 \times 10^4 \) and \( 2.56 \times 10^{-2} \).

To add these, we first need to make sure the exponents are the same:

1. Convert \( 3.2 \times 10^4 \):

   • \( 3.2 \times 10^4 = 32,000 \).

2. Convert \( 2.56 \times 10^{-2} \):

   • \( 2.56 \times 10^{-2} = 0.0256 \).

Now we can add the two numbers: \[ 32,000 + 0.0256 = 32,000.0256 \]

Now let's convert \( 32,000.0256 \) back to scientific notation.

• It’s \( 3.200000256 \times 10^4 \) which we can approximate to: \[ \mathbf{3.20 \times 10^4} \]

b. Subtraction

Now let's subtract \( 4.82 \times 10^{12} \) from \( 1.95 \times 10^{6} \).

Again, we will use the same exponent for comparison:

1. Convert \( 4.82 \times 10^{12} \):

   • Consider \( 4.82 \times 10^{12} = 4,820,000,000,000 \).

2. Convert \( 1.95 \times 10^{6} \):

   • \( 1.95 \times 10^{6} = 1,950,000 \).

Now we can subtract: \[ 1,950,000 - 4,820,000,000,000 = -4,818,050,000,000 \]

To convert \( -4,818,050,000,000 \) back to scientific notation:

• It’s written as: \[ \mathbf{-4.81805 \times 10^{12}} \]

So, the results are:

• a. \( 3.20 \times 10^4 \)
• b. \( -4.81805 \times 10^{12} \)