use 3.2x104 and 1.95 x 106 for steps a,b,c,d. Answers MUST be in correct scientific notation.
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. The sum of 3.2 x 104 and 1.95 x 106 is 2.28 x 106.
B. The difference between 1.95 x 106 and 3.2 x 104 is 1.94 x 106.
C. The product of 3.2 x 104 and 1.95 x 106 is 6.24 x 1010.
D. The quotient of 1.95 x 106 divided by 3.2 x 104 is 6.09 x 101.
A. To add 3.2 x 10^4 and 1.95 x 10^6, first line up the decimal places:
3.2 x 10^4
+ 1.95 x 10^6
____________
Next, since the exponents are the same, we can simply add the coefficients:
1.95 + 3.2 = 5.15
The result is 5.15 x 10^6 in scientific notation.
B. To subtract 1.95 x 10^6 from 3.2 x 10^4, we follow a similar process:
3.2 x 10^4
- 1.95 x 10^6
____________
Again, since the exponents are the same, we can directly subtract the coefficients:
3.2 - 1.95 = 1.25
The result is 1.25 x 10^4 in scientific notation.
C. To multiply 3.2 x 10^4 and 1.95 x 10^6, we multiply the coefficients and add the exponents:
(3.2) * (1.95) = 6.24
10^4 * 10^6 = 10^(4 + 6) = 10^10
The result is 6.24 x 10^10 in scientific notation.
D. To divide 1.95 x 10^6 by 3.2 x 10^4, divide the coefficients and subtract the exponents:
(1.95) / (3.2) = 0.609375
10^6 / 10^4 = 10^(6 - 4) = 10^2
The result is 0.609375 x 10^2 in scientific notation.
To perform the required calculations with scientific notation, follow these steps:
A. Addition
To add numbers in scientific notation, make sure the exponents are the same, then add the coefficients. Finally, adjust the result to proper scientific notation if necessary.
Given:
3.2 x 10^4 (coefficient: 3.2, exponent: 4)
1.95 x 10^6 (coefficient: 1.95, exponent: 6)
Step 1:
Adjust the exponents so they are the same. Moving the decimal point to the right increases the exponent, while moving it to the left decreases the exponent.
3.2 x 10^4 (no change)
1.95 x 10^6 (move the decimal point 2 places to the left) = 0.0195 x 10^6
Step 2:
Add the coefficients: 3.2 + 0.0195 = 3.2195
Step 3:
Adjust the result to correct scientific notation by placing the decimal point after the first non-zero digit and incrementing the exponent accordingly:
3.2195 (move the decimal point 3 places to the right) = 3.2195 x 10^6
Therefore, the sum of 3.2 x 10^4 and 1.95 x 10^6 is 3.2195 x 10^6.
B. Subtraction
Subtracting numbers in scientific notation follows the same steps as addition.
Given:
1.95 x 10^6 (coefficient: 1.95, exponent: 6)
3.2 x 10^4 (coefficient: 3.2, exponent: 4)
Step 1:
Adjust the exponents to be the same.
1.95 x 10^6 (no change)
3.2 x 10^4 (move the decimal point 2 places to the right) = 0.032 x 10^6
Step 2:
Subtract the coefficients: 1.95 - 0.032 = 1.918
Step 3:
Adjust the result to proper scientific notation.
1.918 (move the decimal point 6 places to the right) = 1.918 x 10^6
Therefore, the difference between 1.95 x 10^6 and 3.2 x 10^4 is 1.918 x 10^6.
C. Multiplication
To multiply numbers in scientific notation, multiply the coefficients and add the exponents.
Given:
3.2 x 10^4 (coefficient: 3.2, exponent: 4)
1.95 x 10^6 (coefficient: 1.95, exponent: 6)
Step 1:
Multiply the coefficients: 3.2 x 1.95 = 6.24
Step 2:
Add the exponents: 4 + 6 = 10
Therefore, the product of 3.2 x 10^4 and 1.95 x 10^6 is 6.24 x 10^10.
D. Division
To divide numbers in scientific notation, divide the coefficients and subtract the exponents.
Given:
1.95 x 10^6 (coefficient: 1.95, exponent: 6)
3.2 x 10^4 (coefficient: 3.2, exponent: 4)
Step 1:
Divide the coefficients: 1.95 ÷ 3.2 ≈ 0.609375
Step 2:
Subtract the exponents: 6 - 4 = 2
Therefore, the quotient of 1.95 x 10^6 divided by 3.2 x 10^4 is approximately 0.609375 x 10^2, which can be simplified to 6.09375 x 10^1.