U4L10: PORTFOLIO (modified)
ONLY DO PROBLEM #1 and follow questions a-d only put answers in correct scientific notation. NO NEED TO DO IT ALL…use 3.2x10^4 and 1.95 x 10^6 for steps a,b,c,d. That is it for my portfolio. ANSWERS MUST BE IN SCIENTIFIC NOTATION!!!!
a. Add 3.2 x 10^4 and 1.95 x 10^6
b. Subtract 1.95 x 10^6 and 3.2 x 10^4
c. Multiply 3.2 x 10^4 and 1.95 x 10^6
d. Divide 1.95 x 10^6 and 3.2 x 10^4
a. (3.2 x 10^4) + (1.95 x 10^6) = 1.95 x 10^6
b. (1.95 x 10^6) - (3.2 x 10^4) = 1.9468 x 10^6
c. (3.2 x 10^4) * (1.95 x 10^6) = 6.24 x 10^10
d. (1.95 x 10^6) / (3.2 x 10^4) = 60.9375 x 10^1 = 6.09375 x 10^2
To perform the calculations and express the answers in scientific notation, follow these steps:
a. To add 3.2 x 10^4 and 1.95 x 10^6:
First, align the exponents of the numbers. Since 10^4 is smaller than 10^6, we need to convert 3.2 x 10^4 to the same exponent as 1.95 x 10^6. This can be done by multiplying 3.2 by 100 (10^2).
3.2 x 10^4 becomes 320 x 10^2.
Now, we can add the numbers: 320 x 10^2 + 1.95 x 10^6.
To add them, we add the coefficients and keep the same exponent:
320 + 1.95 = 321.95
So, the answer is 3.2195 x 10^6 in scientific notation.
b. To subtract 1.95 x 10^6 and 3.2 x 10^4:
Again, align the exponents by converting 3.2 x 10^4 to the same exponent as 1.95 x 10^6 (multiply by 100).
3.2 x 10^4 becomes 320 x 10^2.
Now, subtract: 1.95 x 10^6 - 320 x 10^2.
Performing the subtraction, we get: 1.95 x 10^6 - 320 x 10^2 = 1.95 x 10^6 - 0.032 x 10^6
Since the exponents are the same, we subtract the coefficients: 1.95 - 0.032 = 1.918
The answer is 1.918 x 10^6 in scientific notation.
c. To multiply 3.2 x 10^4 and 1.95 x 10^6:
Multiply the coefficients and add the exponents: 3.2 x 1.95 = 6.24
Add the exponents: 10^4 + 10^6 = 10^(4+6) = 10^10
The answer 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
Subtract the exponents: 10^6 - 10^4 = 10^(6-4) = 10^2
The answer is 0.609375 x 10^2 in scientific notation.
a. To add 3.2 x 10^4 and 1.95 x 10^6, we need to make the exponents the same.
3.2 x 10^4 + 1.95 x 10^6
Now, we can add the numbers: 3.2 + 1.95 = 5.15
The exponent remains the same (10^6) since we are adding numbers in scientific notation.
Therefore, the result is 5.15 x 10^6.
b. To subtract 1.95 x 10^6 and 3.2 x 10^4, we need to make the exponents the same.
1.95 x 10^6 - 3.2 x 10^4
Now, we can subtract the numbers: 1.95 - 0.032 = 1.918
The exponent remains the same (10^6) since we are subtracting numbers in scientific notation.
Therefore, the result is 1.918 x 10^6.
c. To multiply 3.2 x 10^4 and 1.95 x 10^6, we can simply multiply the numbers and add the exponents.
(3.2 x 1.95) x (10^4 x 10^6)
Multiplying the numbers gives us: 3.2 x 1.95 = 6.24
Adding the exponents gives us: 10^(4+6) = 10^10
Therefore, the result is 6.24 x 10^10.
d. To divide 1.95 x 10^6 by 3.2 x 10^4, we can divide the numbers and subtract the exponents.
(1.95 / 3.2) x (10^6 / 10^4)
Dividing the numbers gives us: 1.95 / 3.2 ≈ 0.609375
Subtracting the exponents gives us: 10^(6-4) = 10^2
Therefore, the result is 0.609375 x 10^2, which can also be written as 6.09375 x 10^1.
1. incorrect..sum is not difference
2.incorrect it is not a -1.918
3 and 4 look good
I apologize for the mistakes. Let me correct them:
a. To add 3.2 x 10^4 and 1.95 x 10^6:
3.2 x 10^4 + 1.95 x 10^6
To add the numbers, we need to convert one of them to have the same exponent as the other. Let's convert 3.2 x 10^4 to have the same exponent as 1.95 x 10^6. By multiplying 3.2 by 10^2, we get:
3.2 x 10^4 = 320 x 10^2
Now we can add the numbers:
320 x 10^2 + 1.95 x 10^6 = 32000 x 10^2 + 1.95 x 10^6
Combining the coefficients, we get:
32000 + 1.95 = 32295
The exponent remains the same since we are adding numbers in scientific notation. Therefore, the result is:
3.2295 x 10^4.
b. To subtract 1.95 x 10^6 and 3.2 x 10^4:
1.95 x 10^6 - 3.2 x 10^4
Again, let's convert 3.2 x 10^4 to have the same exponent as 1.95 x 10^6:
3.2 x 10^4 = 320 x 10^2
Now we can subtract the numbers:
1.95 x 10^6 - 320 x 10^2 = 1950 x 10^4 - 320 x 10^2
Combining the coefficients, we get:
1950 - 0.032 = 1949.968
The exponent remains the same since we are subtracting numbers in scientific notation. Therefore, the result is:
1.949968 x 10^6.
c. To multiply 3.2 x 10^4 and 1.95 x 10^6:
We need to multiply the coefficients and add the exponents:
(3.2 x 1.95) x (10^4 x 10^6) = 6.24 x (10^4+6) = 6.24 x 10^10.
Therefore, the result is 6.24 x 10^10.
d. To divide 1.95 x 10^6 by 3.2 x 10^4:
We need to divide the coefficients and subtract the exponents:
(1.95 / 3.2) x (10^6 / 10^4) = 0.609375 x (10^6-4) = 0.609375 x 10^2.
Therefore, the result is 0.609375 x 10^2, or in scientific notation, 6.09375 x 10^1.
shorter
a. (3.2 x 10^4) + (1.95 x 10^6) = 1.95 x 10^6
b. (1.95 x 10^6) - (3.2 x 10^4) = 1.91768 x 10^6
c. (3.2 x 10^4) * (1.95 x 10^6) = 6.24 x 10^10
d. (1.95 x 10^6) / (3.2 x 10^4) = 6.09375 x 10^1