In this problem, you will practice added, subtracting, multiplying, and dividing numbers written in scientific notation. For each part, use the following numbers.
3.2 x 10^4, 1.95 x 10^6, 8.03 x 10^-8, 2.56 x 10^-2, 4.82 x 10^12
Choose one of the scientific numbers from the list and add it to 32.8. Show your work.
Let's choose the scientific number 3.2 x 10^4 and add it to 32.8.
To add these numbers, we need to adjust the scientific notation of 3.2 x 10^4 and 32.8 so that they have the same exponent.
32.8 can be written in scientific notation as 3.28 x 10^1.
Now, we can add the two numbers:
(3.2 x 10^4) + (3.28 x 10^1) = (3.2 + 3.28) x 10^4
Adding the values inside the parentheses:
= 6.48 x 10^4
Therefore, when we add 3.2 x 10^4 to 32.8, the result is 6.48 x 10^4.
To add a number in scientific notation to a regular number, we need to convert the regular number into scientific notation. Let's choose the number 32.8 and add it to 3.2 x 10^4.
First, we convert 32.8 into scientific notation:
32.8 = 3.28 x 10^1
Now, we can add the two numbers:
(3.2 x 10^4) + (3.28 x 10^1)
To add numbers in scientific notation, we need to have the same exponent. Let's convert 3.28 x 10^1 to match the exponent of 10^4:
(3.28 x 10^1) = (0.328 x 10^2)
Now, we can add the numbers:
(3.2 x 10^4) + (0.328 x 10^2)
To add, we only add the coefficients and keep the same exponent:
3.2 + 0.328 = 3.528
Finally, the sum is:
3.528 x 10^4
To add a number written in scientific notation to a regular number, we need to convert the regular number into scientific notation. In this case, we want to add 32.8 to a number from the list:
Let's choose the number 3.2 x 10^4 from the list. To add it to 32.8, we need to convert 32.8 into scientific notation.
To convert 32.8 into scientific notation, we count the number of decimal places we move the decimal point to get a number between 1 and 10. In this case, we move it one place to the left to get 3.28. Therefore, 32.8 is 3.28 x 10^1.
Now, we can add the numbers in scientific notation:
3.2 x 10^4 + 3.28 x 10^1 = (3.2 + 3.28) x 10^4 = 6.48 x 10^4
So, adding 3.2 x 10^4 to 32.8 equals 6.48 x 10^4.