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 two of the scientific numbers from the list and add them. Show your
work.
Let's choose 3.2 x 10^4 and 1.95 x 10^6 to add.
To add these numbers, we first need to make sure they have the same exponent. In this case, we can rewrite 3.2 x 10^4 as 0.32 x 10^5, since multiplying by 10^1 is the same as moving the decimal point one place to the right.
Now we can add the numbers:
0.32 x 10^5 + 1.95 x 10^6
To add the numbers, we can add the coefficients:
0.32 + 1.95 = 2.27
And the exponent remains the same:
10^5
So the sum of 3.2 x 10^4 and 1.95 x 10^6 is 2.27 x 10^5.
To add two numbers in scientific notation, we first need to make sure that the exponents of the numbers are the same. If they are not, we can adjust one or both of the numbers so that they have the same exponent.
Let's choose the numbers 3.2 x 10^4 and 4.82 x 10^12 to add.
Step 1: Adjust the exponents so that they are the same.
We can adjust 3.2 x 10^4 to 3.2 x 10^12 by multiplying it by 10^8. This will give us 3.2 x 10^(4+8) = 3.2 x 10^12.
Step 2: Add the adjusted numbers.
Now that the exponents are the same, we can simply add the coefficients:
3.2 x 10^12 + 4.82 x 10^12 = (3.2 + 4.82) x 10^12 = 8.02 x 10^12.
So the sum of 3.2 x 10^4 and 4.82 x 10^12 is 8.02 x 10^12.
To add two numbers written in scientific notation, you need to first ensure that the exponents are the same. If the exponents are different, you need to adjust one or both of the numbers accordingly.
Let's choose the numbers 3.2 x 10^4 and 1.95 x 10^6 to add.
Step 1: Adjust the exponents
In this case, we need to adjust the exponent of 3.2 x 10^4 to match the exponent of 1.95 x 10^6. To do this, we can move the decimal point of 3.2 two places to the right to get 320. Since we moved the decimal point two places to the right, we need to decrease the exponent by 2. Therefore, 3.2 x 10^4 becomes 320 x 10^2.
Step 2: Add the numbers
Now that the exponents are the same, we can simply add the two numbers:
320 x 10^2 + 1.95 x 10^6 = 320 x 10^2 + 195 x 10^4
Step 3: Perform the addition
To add the numbers, we add the coefficients (320 and 195) and keep the common base (10) raised to the exponent (2). Therefore,
320 x 10^2 + 195 x 10^4 = 515 x 10^2
Step 4: Simplify the result
If we express the final answer in scientific notation, we need to make sure the coefficient is between 1 and 10. In this case, the coefficient, 515, is already between 1 and 10. Therefore, the final answer is:
515 x 10^2
So, adding 3.2 x 10^4 and 1.95 x 10^6 gives us 515 x 10^2.