use 3.2x104 and 1.95 x 106 for steps a,b,c,d. Answers MUST be in correct scientific notation. show work
A. Add 3.2 x 104 and 1.95 x 106
B. Subtract 1.95 x 106 and 3.2 x 104
C. Multiply 3.2 x 104 and 1.95 x 106
D. Divide 1.95 x 106 and 3.2 x 104
A. 3.2 x 104 + 1.95 x 106 = (3.2 + 1.95) x 106 = 5.15 x 106
B. 1.95 x 106 - 3.2 x 104 = (1.95 - 0.032) x 106 = 1.918 x 106
C. 3.2 x 104 * 1.95 x 106 = (3.2 * 1.95) x (104 + 6) = 6.24 x 1010
D. 1.95 x 106 / 3.2 x 104 = (1.95 / 3.2) x (106 - 104) = 0.609375 x 102 = 6.09375 x 101
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.
A. To add 3.2 x 104 and 1.95 x 106, we can align the decimal points by moving the decimal point in 3.2 x 104 one place to the right, making it 32 x 103. Now we add:
32 x 103 + 1.95 x 106 = 0.032 x 106 + 1.95 x 106 = (0.032 + 1.95) x 106 = 1.982 x 106
Therefore, the sum of 3.2 x 104 and 1.95 x 106 is 1.982 x 106.
B. To subtract 3.2 x 104 from 1.95 x 106, we can align the decimal points as before:
1.95 x 106 - 0.032 x 106 = (1.95 - 0.032) x 106 = 1.918 x 106
Therefore, the difference between 1.95 x 106 and 3.2 x 104 is 1.918 x 106.
C. To multiply 3.2 x 104 and 1.95 x 106, we multiply their coefficients and add their exponents:
3.2 x 104 x 1.95 x 106 = (3.2 x 1.95) x (104 + 106) = 6.24 x 1010
Therefore, the product of 3.2 x 104 and 1.95 x 106 is 6.24 x 1010.
D. To divide 1.95 x 106 by 3.2 x 104, we divide their coefficients and subtract their exponents:
1.95 x 106 ÷ 3.2 x 104 = (1.95 ÷ 3.2) x (106 - 104) = 0.609375 x 102
However, we need to express the result in scientific notation, so we can rewrite it as:
0.609375 x 102 = 6.09375 x 10-1+2 = 6.09375 x 101
Therefore, the quotient of 1.95 x 106 divided by 3.2 x 104 is 6.09375 x 101.