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.
3.2 ✕ 10^4 + 1.95 ✕ 10^6
= (3.2 + 1.95) ✕ 10^4 (Since they have the same power of 10)
= 5.15 ✕ 10^4
Choose two of the scientific numbers from the list and subtract them. Show your work.
4.82 ✕ 10^12 - 2.56 ✕ 10^-2
= (4.82 ✕ 10^12) - (2.56 ✕ 10^-2)
= 4.82 ✕ 10^12 - 0.0256 ✕ 10^12 (Converting 2.56 ✕ 10^-2 to scientific notation by multiplying by 10^12)
= 4.7944 ✕ 10^12
Choose two of the scientific numbers from the list and multiply them. Show your work.
3.2 ✕ 10^4 * 8.03 ✕ 10^-8
= (3.2 * 8.03) ✕ (10^4 * 10^-8) (Using the properties of exponents)
= (25.696) ✕ (10^(-4+(-8))) (Adding the exponents)
= 25.696 ✕ 10^-12
Choose two of the scientific numbers from the list and divide them. Show your work.
2.56 ✕ 10^-2 / 8.03 ✕ 10^-8
= (2.56 / 8.03) ✕ (10^(-2-(-8))) (Using the properties of exponents)
= (0.319102) ✕ (10^(-2+8)) (Subtracting the exponents)
= 0.319102 ✕ 10^6
Choose one of the scientific numbers from the list and add it to 32.8. Show your work.
3.2 ✕ 10^4 + 32.8
= 3.2 ✕ 10^4 + 32.8 ✕ 10^0 (Converting 32.8 to scientific notation by multiplying by 10^0)
= 3.2 ✕ 10^4 + 32.8 ✕ 1 (Multiplying by 1 does not change the value)
= 3.2 ✕ 10^4 + 32.8
(The answer is not in scientific notation since 32.8 is a decimal number and does not require the use of powers of 10)
Choose one of the scientific numbers from the list and multiply it by 256.7. Show your work.
8.03 ✕ 10^-8 * 256.7
= 8.03 ✕ 256.7 ✕ 10^-8 (Multiplying the decimal part)
= 2065.501 ✕ 10^-8
= 2.065501 ✕ 10^-5
To add two scientific numbers:
Let's choose 3.2 × 10^4 and 1.95 × 10^6.
3.2 × 10^4 + 1.95 × 10^6 = (3.2 + 0.000000195) × 10^4 = 3.200000195 × 10^4.
Therefore, the sum of 3.2 × 10^4 and 1.95 × 10^6 is 3.200000195 × 10^4.
To subtract two scientific numbers:
Let's choose 2.56 × 10^-2 and 4.82 × 10^12.
4.82 × 10^12 - 2.56 × 10^-2 = (4.82 - 0.0000000000256) × 10^12 = 4.8199999999744 × 10^12.
Therefore, the difference between 4.82 × 10^12 and 2.56 × 10^-2 is 4.8199999999744 × 10^12.
To multiply two scientific numbers:
Let's choose 1.95 × 10^6 and 2.56 × 10^-2.
(1.95 × 2.56) × (10^6 × 10^-2) = 4.992 × 10^4.
Therefore, the product of 1.95 × 10^6 and 2.56 × 10^-2 is 4.992 × 10^4.
To divide two scientific numbers:
Let's choose 8.03 × 10^-8 and 3.2 × 10^4.
(8.03 ÷ 3.2) × (10^-8 ÷ 10^4) = 2.509375 × 10^-12.
Therefore, the division of 8.03 × 10^-8 and 3.2 × 10^4 is 2.509375 × 10^-12.
To add a scientific number to a non-scientific number:
Let's choose 2.56 × 10^-2 and 32.8.
2.56 × 10^-2 + 32.8 = 32.800256.
Therefore, the sum of 2.56 × 10^-2 and 32.8 is 32.800256.
To multiply a scientific number by a non-scientific number:
Let's choose 4.82 × 10^12 and 256.7.
4.82 × 10^12 × 256.7 = 1.238094 × 10^15.
Therefore, the product of 4.82 × 10^12 and 256.7 is 1.238094 × 10^15.
To solve the problems in Part 1 of the Scientific Notation portfolio, we will use the rules of scientific notation. Here are the steps to follow for each problem:
1. Addition: To add two numbers in scientific notation, make sure their exponents are the same. If they are not, adjust one of the numbers so that the exponents match. Then, add the coefficients while keeping the exponent the same.
2. Subtraction: Similar to addition, adjust the exponents of the two numbers so that they match. Then, subtract the coefficients while keeping the exponent the same.
3. Multiplication: Multiply the coefficients of the two numbers, and add the exponents.
4. Division: Divide the coefficients of the two numbers, and subtract the exponents.
Here's how you would solve each problem:
Choose two of the scientific numbers from the list and add them:
Let's say we choose 3.2 ✕ 10^4 and 1.95 ✕ 10^6. To add them, we need to adjust the exponent of the first number to match the second number. We can rewrite 3.2 ✕ 10^4 as 0.032 ✕ 10^6. Now, we can add the coefficients: 0.032 + 1.95 = 1.982. The exponent remains 6. Therefore, the sum of 3.2 ✕ 10^4 and 1.95 ✕ 10^6 is 1.982 ✕ 10^6.
Choose two of the scientific numbers from the list and subtract them:
Let's say we choose 8.03 ✕ 10^-8 and 2.56 ✕ 10^-2. Again, we need to adjust the exponents to match. We can rewrite 8.03 ✕ 10^-8 as 0.0000000803 ✕ 10^-2. Now, we can subtract the coefficients: 0.0000000803 - 2.56 = -2.5599999197. The exponent remains -2. Therefore, the difference of 8.03 ✕ 10^-8 and 2.56 ✕ 10^-2 is -2.5599999197 ✕ 10^-2.
Choose two of the scientific numbers from the list and multiply them:
Let's say we choose 4.82 ✕ 10^12 and 3.2 ✕ 10^4. To multiply them, we multiply the coefficients: 4.82 × 3.2 = 15.424. Then, we add the exponents: 12 + 4 = 16. Therefore, the product of 4.82 ✕ 10^12 and 3.2 ✕ 10^4 is 15.424 ✕ 10^16.
Choose two of the scientific numbers from the list and divide them:
Let's say we choose 1.95 ✕ 10^6 and 2.56 ✕ 10^-2. To divide them, divide the coefficients: 1.95 ÷ 2.56 ≈ 0.76171875. Then, subtract the exponents: 6 - (-2) = 8. Therefore, the quotient of 1.95 ✕ 10^6 divided by 2.56 ✕ 10^-2 is approximately 0.76171875 ✕ 10^8.
Choose one of the scientific numbers from the list and add it to 32.8:
Let's say we choose 8.03 ✕ 10^-8. To add it to 32.8, we don't need to convert 32.8 into scientific notation since it doesn't have an exponent. Add the coefficient of the scientific number and 32.8: 0.0000000803 + 32.8 ≈ 32.8000000803. Therefore, the sum of 8.03 ✕ 10^-8 and 32.8 is approximately 32.8000000803.
Choose one of the scientific numbers from the list and multiply it by 256.7:
Let's say we choose 2.56 ✕ 10^-2. To multiply it by 256.7, we don't need to convert 256.7 into scientific notation as it doesn't have an exponent. Multiply the coefficient of the scientific number by 256.7: 2.56 × 256.7 ≈ 658.112. Then add the exponent of the scientific number (in this case, -2): 658.112 ✕ 10^-2. Therefore, the product of 2.56 ✕ 10^-2 and 256.7 is approximately 658.112 ✕ 10^-2.
Remember to show your work in your worksheet by writing the equations, solving them step by step, and writing the final answers.