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.
1. Addition:
To add two numbers in scientific notation, you need to make sure that their exponents are the same. Once the exponents are aligned, you can simply add the corresponding coefficients.
Let's choose 3.2 ✕ 10^4 and 2.56 ✕ 10^-2:
3.2 ✕ 10^4 + 2.56 ✕ 10^-2
To align the exponents, we can rewrite 2.56 ✕ 10^-2 as 0.0256 ✕ 10^4.
Now we can add the coefficients: 3.2 + 0.0256 = 3.2256.
Therefore, 3.2 ✕ 10^4 + 2.56 ✕ 10^-2 = 3.2256 ✕ 10^4.
2. Subtraction:
Similarly, to subtract two numbers in scientific notation, you need to align their exponents. Then, you can subtract the corresponding coefficients.
Let's choose 1.95 ✕ 10^6 and 4.82 ✕ 10^12:
1.95 ✕ 10^6 - 4.82 ✕ 10^12
To align the exponents, we need to convert 1.95 ✕ 10^6 to scientific notation with an exponent of 12: 1.95 ✕ 10^6 = 0.00000000195 ✕ 10^12.
Now we can subtract the coefficients: 0.00000000195 - 4.82 = -4.819999999995.
Therefore, 1.95 ✕ 10^6 - 4.82 ✕ 10^12 = -4.82 ✕ 10^12 (approximated to 2 significant figures).
To add two scientific numbers, we need to ensure that the powers of 10 are the same for both numbers. Let's choose 3.2 ✕ 10^4 and 8.03 ✕ 10^-8.
First, we need to adjust the powers of 10 to be the same. Since 10^-8 is a smaller power than 10^4, we can convert 3.2 ✕ 10^4 to scientific notation with a power of 10^-8.
3.2 ✕ 10^4 = 0.00000032 ✕ 10^8 (divide the coefficient by 10^4 and multiply the power of 10 by 10^4)
Now we can add the two numbers:
0.00000032 ✕ 10^8 + 8.03 ✕ 10^-8 = (0.00000032 + 8.03) ✕ 10^-8 (add the coefficients)
= 8.03000032 ✕ 10^-8
Therefore, the sum of 3.2 ✕ 10^4 and 8.03 ✕ 10^-8 is 8.03000032 ✕ 10^-8.
To subtract two scientific numbers, we follow a similar process.
Let's choose 4.82 ✕ 10^12 and 2.56 ✕ 10^-2.
Again, we adjust the powers of 10 to be the same. Since 10^12 is a larger power than 10^-2, we can convert 2.56 ✕ 10^-2 to scientific notation with a power of 10^12.
2.56 ✕ 10^-2 = 2560000000000 ✕ 10^12 (multiply the coefficient by 10^14 and divide the power of 10 by 10^-2)
Now we can subtract the two numbers:
4.82 ✕ 10^12 - 2560000000000 ✕ 10^12 = (4.82 - 2560000000000) ✕ 10^12 (subtract the coefficients)
= -2559999999995.18 ✕ 10^12
Therefore, the difference of 4.82 ✕ 10^12 and 2.56 ✕ 10^-2 is -2559999999995.18 ✕ 10^12.
To add or subtract numbers written in scientific notation, we need to make sure that the exponents are the same. Here's how we can do it:
Let's choose the numbers 3.2 × 10^4 and 8.03 × 10^-8 to add.
Step 1: Align the exponents.
Since 10^4 is the largest exponent, we need to rewrite 8.03 × 10^-8 as a number with an exponent of 10^4.
To do this, we shift the decimal point 12 places to the right (10^4 - (-8) = 10^12).
8.03 × 10^-8 becomes 0.0000000000803 × 10^12.
Now both numbers have an exponent of 10^4.
Step 2: Perform the addition.
(3.2 × 10^4) + (0.0000000000803 × 10^12)
Remember, when adding or subtracting numbers in scientific notation, we only operate on the numerical part and keep the common exponent.
3.2 + 0.0000000000803 = 3.2000000000803
The sum is 3.2000000000803 × 10^4.
Let's now choose the numbers 1.95 × 10^6 and 2.56 × 10^-2 to subtract.
Step 1: Align the exponents.
Since 10^6 is the largest exponent, we need to rewrite 2.56 × 10^-2 as a number with an exponent of 10^6.
To do this, we shift the decimal point 8 places to the right (10^6 - (-2) = 10^8).
2.56 × 10^-2 becomes 0.000000256 × 10^8.
Now both numbers have an exponent of 10^6.
Step 2: Perform the subtraction.
(1.95 × 10^6) - (0.000000256 × 10^8)
Again, we only operate on the numerical part.
1.95 - 0.000000256 = 1.949999744
The difference is 1.949999744 × 10^6.
Remember to save your worksheet with your answers and submit it for grading.