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 one of the scientific numbers from the list and subtract it from 1,845.19 Show your work.

Answer 1

To solve the problem, I will select the number \( 1.95 \times 10^6 \) from the list and subtract it from 1,845.19.

Step 1: Convert 1,845.19 to scientific notation.

To express 1,845.19 in scientific notation:

• Move the decimal point 3 places to the left: \( 1.84519 \times 10^3 \)

Step 2: Set up the subtraction.

We need to convert \( 1.95 \times 10^6 \) to a form that allows us to subtract.

To do this, let's express \( 1.84519 \times 10^3 \) in terms of \( 10^6 \):

• To do this, we multiply by \( 10^{3} \) so we need to convert it to \( 10^6 \):
• \( 1.84519 \times 10^3 \) can be written as: \( 1.84519 \times 10^3 = 0.00184519 \times 10^6 \) (by moving the decimal 3 places to the left)

Step 3: Perform the subtraction.

Now we have:

• \( 1.95 \times 10^6 \)
• \( 0.00184519 \times 10^6 \)

Now we can do the subtraction: \[ 1.95 \times 10^6 - 0.00184519 \times 10^6 = (1.95 - 0.00184519) \times 10^6 \]

Calculating: \[ 1.95 - 0.00184519 = 1.94815481 \]

So we have: \[ 1.94815481 \times 10^6 \]

Step 4: Write the final answer.

The result of subtracting \( 1.95 \times 10^6 \) from 1,845.19 is: \[ 1.94815481 \times 10^6 \]

This is the answer written in scientific notation.