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 number 3.2 x 10^4 and add it to 32.8.
First, we need to convert 32.8 to scientific notation. Since 32.8 is already in decimal form, we can express it as 3.28 x 10^1.
Now we can add 3.2 x 10^4 and 3.28 x 10^1:
3.2 x 10^4 + 3.28 x 10^1 = 3.2 x 10000 + 3.28 x 10 = 32000 + 32.8
To combine the two numbers, the exponents of 10 need to be the same, so we need to rewrite 32000 as a number multiplied by 10 raised to an exponent:
32000 = 3.2 x 10000 = 3.2 x 10^4
Now we can add the numbers:
3.2 x 10^4 + 3.28 x 10^1 = 3.2 x 10^4 + 3.2 x 10^1 = 3.2 x 10^4 + 3.2 x 10^4 = 6.4 x 10^4
Therefore, when we add 3.2 x 10^4 to 32.8, we get 6.4 x 10^4.
Let's choose the scientific number 3.2 x 10^4 and add it to 32.8.
Step 1: Convert 32.8 to scientific notation.
To convert 32.8 to scientific notation, we move the decimal point to the right until we have a number between 1 and 10. In this case, 32.8 can be written as 3.28 x 10^1.
Step 2: Add the two 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.
Therefore, when we add 3.2 x 10^4 to 32.8, we get 6.48 x 10^4.
To add a number in scientific notation to a regular number, you first need to convert the regular number to scientific notation if it is not already in that form.
In this case, you have the scientific number 3.2 x 10^4 and you need to add it to 32.8.
First, let's convert 32.8 to scientific notation. Since 32.8 is not a power of 10, we need to move the decimal point to the left by one position to get a number between 1 and 10. This gives us 3.28 x 10^1.
Now that both numbers are in scientific notation, we can add them together. To add numbers in scientific notation, the exponents must be the same. If they are not the same, you need to adjust one or both numbers to make the exponents equal.
In this case, the exponent for 3.2 x 10^4 is 4, and the exponent for 3.28 x 10^1 is 1. We need to adjust the second number to match the exponent of the first number.
To do this, we need to move the decimal point in 3.28 x 10^1 two places to the right to get 3.28 x 10^3. This adjustment aligns the exponents and allows us to add the numbers.
Now we can add the numbers:
3.2 x 10^4 + 3.28 x 10^3 = (3.2 + 3.28) x 10^4 = 6.48 x 10^4
Therefore, the result of adding 3.2 x 10^4 to 32.8 is 6.48 x 10^4.