Scientific Notation Portfolio

Question

Use this worksheet to record your answers to the Scientific Notation portfolio activities. There are 3 parts, so make sure you scroll down to see all of them. When you are finished, save your worksheet with your answers and submit it for a portfolio grade. By showing your work, we are asking you to write the equation and then solve and write the answer.

Part 1: Use the following numbers.

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

Answer 1

To subtract two numbers in scientific notation, they must first have the same exponent. Here's how to do that step-by-step using the numbers \( 1.95 \times 10^6 \) and \( 3.2 \times 10^4 \).

Step 1: Write the numbers

• \( A = 1.95 \times 10^6 \)
• \( B = 3.2 \times 10^4 \)

Step 2: Adjust the exponent of \( B \) to match \( A \)

Since \( A \) has the exponent of \( 10^6 \), we need to convert \( B \) from \( 10^4 \) to \( 10^6 \).

To convert \( 3.2 \times 10^4 \) to a base of \( 10^6 \): \[ B = 3.2 \times 10^4 = 3.2 \times 10^4 \times \frac{10^2}{10^2} = 3.2 \times 10^6 \div 100 = 0.032 \times 10^6 \]

Step 3: Subtract the numbers

Now that both numbers have the same exponent, we can subtract: \[ A - B = (1.95 \times 10^6) - (0.032 \times 10^6) \]

Calculating: \[ = (1.95 - 0.032) \times 10^6 \] \[ = 1.918 \times 10^6 \]

So the final answer for the subtraction of \( 1.95 \times 10^6 \) and \( 3.2 \times 10^4 \) is: \[ \boxed{1.918 \times 10^6} \]