Scientific Notation Portfolio
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 add them. Show your work.
Choose two of the scientific numbers from the list and subtract them. Show your work.
Choose two of the scientific numbers from the list and multiply them. Show your work.
Choose two of the scientific numbers from the list and divide them. Show your work.
Choose one of the scientific numbers from the list and add it to 32.8. Show your work.
Choose one of the scientific numbers from the list and multiply it by 256.7. Show your work.
Part 1:
Choose two of the scientific numbers from the list and add them. Show your work.
(1.95 x 10^6) + (4.82 x 10^12) = 1.95 x 10^6 + 4.82 x 10^12 = 1.95 x 10^6 + 482 x 10^10 (rewrite in scientific notation) = (1.95 + 482) x 10^10 (add the coefficients and keep the same exponent) = 483.95 x 10^10 = 4.8395 x 10^12 (rewrite in scientific notation)
Choose two of the scientific numbers from the list and subtract them. Show your work.
(3.2 x 10^4) - (2.56 x 10^-2) = 3.2 x 10^4 - 0.0256 x 10^0 (rewrite in scientific notation) = 3.2 x 10^4 - 0.0256 (remove the exponent of 10) = 3.1999744 x 10^4 (perform subtraction) = 3.2 x 10^4 (rewrite in scientific notation)
Choose two of the scientific numbers from the list and multiply them. Show your work.
(8.03 x 10^-8) * (2.56 x 10^-2) = (8.03 * 2.56) x 10^(-8 + -2) (multiply the coefficients and add the exponents) = 20.5648 x 10^-10 = 2.05648 x 10^-9 (rewrite in scientific notation)
Choose two of the scientific numbers from the list and divide them. Show your work.
(1.95 x 10^6) / (2.56 x 10^-2) = (1.95 / 2.56) x 10^(6 - -2) (divide the coefficients and subtract the exponents) = 0.76171875 x 10^8 = 7.6171875 x 10^7 (rewrite in scientific notation)
Choose one of the scientific numbers from the list and add it to 32.8. Show your work.
(3.2 x 10^4) + 32.8 = 3.2 x 10^4 + 32.8 x 10^0 (rewrite in scientific notation) = 32.8 x 10^0 + 3.2 x 10^4 (change the order of the terms to simplify) = 32.8 x 10^0 + 3200 x 10^1 (rewrite 3.2 x 10^4 as 3200 x 10^1) = (32.8 + 3200) x 10^1 (add the coefficients and keep the same exponent) = 3232.8 x 10^1 = 3.2328 x 10^3 (rewrite in scientific notation)
Choose one of the scientific numbers from the list and multiply it by 256.7. Show your work.
(4.82 x 10^12) * 256.7 = 4.82 x 10^12 * 256.7 x 10^0 (rewrite in scientific notation) = 4.82 x 256.7 x 10^(12+0) (multiply the coefficients and add the exponents) = 1237.374 x 10^12 = 1.237374 x 10^15 (rewrite in scientific notation)
To add two scientific numbers, we must have the same exponent. Let's choose 3.2 x 10^4 and 8.03 x 10^-8.
3.2 x 10^4 + 8.03 x 10^-8 = (3.2 + 0.0000000803) x 10^4 = 3.2000000803 x 10^4
To subtract two scientific numbers, we also need the same exponent. Let's choose 1.95 x 10^6 and 4.82 x 10^12.
1.95 x 10^6 - 4.82 x 10^12 = (0.00000000000195 - 4820000000000) x 10^6 = -4819999999999.99 x 10^6
To multiply two scientific numbers, we can simply multiply the coefficients and add the exponents. Let's choose 3.2 x 10^4 and 2.56 x 10^-2.
(3.2 x 10^4) * (2.56 x 10^-2) = (3.2 * 2.56) x (10^4 * 10^-2) = 8.192 x 10^2
To divide two scientific numbers, we can divide the coefficients and subtract the exponents. Let's choose 3.2 x 10^4 and 2.56 x 10^-2 again.
(3.2 x 10^4) / (2.56 x 10^-2) = (3.2 / 2.56) x (10^4 / 10^-2) = 1.25 x 10^6
To add a scientific number to 32.8, we can convert 32.8 into scientific notation. Let's choose 1.95 x 10^6.
1.95 x 10^6 + 32.8 = 1.95 x 10^6 + 3.28 x 10^1 = (1.95 + 0.0328) x 10^6 = 1.9828 x 10^6
To multiply a scientific number by 256.7, we can simply multiply the coefficient and add the exponent. Let's choose 8.03 x 10^-8.
(8.03 x 10^-8) * 256.7 = (8.03 * 256.7) x 10^-8 = 2062.701 x 10^-8 = 2.062701 x 10^-5
To complete this portfolio activity, you will need to perform various operations using scientific notation. Here's how you can solve each part:
Part 1: Using the given list of scientific numbers, you need to choose two numbers and perform the requested operations:
1. Addition: Add two scientific numbers. For example, let's choose 3.2 ✕ 10^4 and 1.95 ✕ 10^6.
- Write down the two numbers: 3.2 ✕ 10^4 + 1.95 ✕ 10^6.
- Now, to add these numbers, the exponents need to be the same. Rewrite them in the same exponent form.
- 3.2 ✕ 10^4 becomes 0.32 ✕ 10^5 (because 10^4 = 10^5 divided by 10).
- Adding the numbers with the same exponent gives us: 0.32 ✕ 10^5 + 1.95 ✕ 10^6 = 2.28 ✕ 10^6.
2. Subtraction: Subtract two scientific numbers. Let's choose 8.03 ✕ 10^-8 and 2.56 ✕ 10^-2.
- Write down the two numbers: 8.03 ✕ 10^-8 - 2.56 ✕ 10^-2.
- To subtract these numbers, we need to make the exponents the same. Rewrite them in the same exponent form.
- 2.56 ✕ 10^-2 becomes 256 ✕ 10^-8 (because 10^-2 = 10^-8 multiplied by 10^6).
- Subtracting the numbers with the same exponent gives us: 8.03 ✕ 10^-8 - 256 ✕ 10^-8 = -247.97 ✕ 10^-8.
3. Multiplication: Multiply two scientific numbers. Let's choose 4.82 ✕ 10^12 and 2.56 ✕ 10^-2.
- Write down the two numbers: (4.82 ✕ 10^12) × (2.56 ✕ 10^-2).
- Multiply the two numbers: (4.82 × 2.56) ✕ (10^12 × 10^-2).
- The multiplication of the decimal parts gives us: (4.82 × 2.56) = 12.3712.
- For the exponents, we add them together: 10^12 × 10^-2 = 10^(12-2) = 10^10.
- Putting everything together: (4.82 ✕ 10^12) × (2.56 ✕ 10^-2) = 12.3712 ✕ 10^10.
4. Division: Divide two scientific numbers. Let's choose 1.95 ✕ 10^6 and 2.56 ✕ 10^-2.
- Write down the two numbers: (1.95 ✕ 10^6) ÷ (2.56 ✕ 10^-2).
- Divide the decimal parts: (1.95 ÷ 2.56).
- For the exponents, we subtract them. 10^6 divided by 10^-2 is equal to 10^(6+2) = 10^8.
- Combining everything: (1.95 ✕ 10^6) ÷ (2.56 ✕ 10^-2) = 0.76171875 ✕ 10^8.
5. Addition with a non-scientific number: Choose one scientific number from the list and add it to 32.8.
- Let's choose 3.2 ✕ 10^4 and add it to 32.8.
- Simply add the two numbers together: 3.2 ✕ 10^4 + 32.8 = 32032.8.
6. Multiplication with a non-scientific number: Choose one scientific number from the list and multiply it by 256.7.
- Let's choose 2.56 ✕ 10^-2 and multiply it by 256.7.
- Multiply the two numbers: (2.56 × 256.7).
- The multiplication gives us: 657.152.
Remember to record your answers and show your work for each calculation in your worksheet.