Sure, let's work through each step using the given numbers and converting the answers to correct scientific notation.
A. Adding 3.2 x 10^4 and 1.95 x 10^6:
To add these numbers, we need to align the decimal points. Since both numbers have the same exponent part (10^4 and 10^6), we can directly add the coefficients.
3.2 x 10^4 + 1.95 x 10^6 = (3.2 + 1.95) x 10^6
Now, calculate the sum of the coefficients:
3.2 + 1.95 = 5.15
Therefore, the answer is 5.15 x 10^6 in scientific notation.
B. Subtracting 1.95 x 10^6 and 3.2 x 10^4:
Again, we align the decimal points since both numbers have the same exponent part.
1.95 x 10^6 - 3.2 x 10^4 = (1.95 - 0.032) x 10^6
Now, calculate the difference of the coefficients:
1.95 - 0.032 = 1.918
Therefore, the answer is 1.918 x 10^6 in scientific notation.
C. Multiplying 3.2 x 10^4 and 1.95 x 10^6:
To multiply these numbers, we multiply the coefficients and add the exponents.
3.2 x 10^4 * 1.95 x 10^6 = (3.2 * 1.95) x 10^(4 + 6)
Calculate the product of the coefficients:
3.2 * 1.95 = 6.24
Add the exponents:
4 + 6 = 10
Therefore, the answer is 6.24 x 10^10 in scientific notation.
D. Dividing 1.95 x 10^6 by 3.2 x 10^4:
To divide these numbers, we divide the coefficients and subtract the exponents.
(1.95 x 10^6) / (3.2 x 10^4) = (1.95 / 3.2) x 10^(6 - 4)
Calculate the quotient of the coefficients:
1.95 / 3.2 = 0.609375
Subtract the exponents:
6 - 4 = 2
Therefore, the answer is 0.609375 x 10^2 in scientific notation, which is equivalent to 6.09375 x 10^1.