U4L10: PORTFOLIO (modified)
ONLY DO PROBLEM #1 and follow questions a-d only. NO NEED TO DO IT ALL…use 3.2x10^4 and 1.95 x 10^6 for steps a,b,c,d. Answers MUST be in correct scientific notation. That is it for portfolio
Add 3.2x10^4 and 1.95 x 10^6
Subtract 1.95 x 10^6 and 3.2 x 10^4
Multiply 3.2 x 10^4 and 1.95 x 10^6
Divide 1.95 x 10^6 and 3.2 x 10^4
a) To add 3.2x10^4 and 1.95x10^6, simply add the coefficients (3.2 + 1.95) and keep the same exponent (10^4):
3.2x10^4 + 1.95x10^6 = 5.15x10^6
b) To subtract 1.95x10^6 and 3.2x10^4, again subtract the coefficients (1.95 -3.2) and keep the same exponent:
1.95x10^6 - 3.2x10^4 = -1.25x10^6 (Negative exponent means the number is in scientific notation)
c) To multiply 3.2x10^4 and 1.95x10^6, multiply the coefficients (3.2 * 1.95) and add the exponents (10^4 + 10^6):
3.2x10^4 * 1.95x10^6 = 6.24x10^10
d) To divide 1.95x10^6 and 3.2x10^4, divide the coefficients (1.95 / 3.2) and subtract the exponents (10^6 - 10^4):
1.95x10^6 / 3.2x10^4 = 0.609375x10^2
Now, we can simplify this further by converting 0.609375 to scientific notation:
0.609375 = 6.09375 x 10^-1
Therefore:
1.95x10^6 / 3.2x10^4 = 6.09375x10^-1 x 10^2 = 6.09375x10^1
a) To add 3.2 x 10^4 and 1.95 x 10^6, we need to make sure that the exponents are the same. In this case, we can rewrite 3.2 x 10^4 as 0.32 x 10^5:
3.2 x 10^4 + 1.95 x 10^6 = 0.32 x 10^5 + 1.95 x 10^6
Now, let's add the two numbers together:
0.32 x 10^5 + 1.95 x 10^6 = 2.27 x 10^6
So the sum is 2.27 x 10^6.
b) To subtract 1.95 x 10^6 from 3.2 x 10^4, we can rewrite 3.2 x 10^4 as 0.032 x 10^6:
3.2 x 10^4 - 1.95 x 10^6 = 0.032 x 10^6 - 1.95 x 10^6
Now, let's subtract the two numbers:
0.032 x 10^6 - 1.95 x 10^6 = -1.918 x 10^6
So the difference is -1.918 x 10^6.
c) To multiply 3.2 x 10^4 and 1.95 x 10^6, we can multiply the numbers and add the exponents:
(3.2 x 10^4) * (1.95 x 10^6) = (3.2 * 1.95) x (10^4 * 10^6) = 6.24 x 10^10
So the product 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 x 10^6) / (3.2 x 10^4) = (1.95 / 3.2) x (10^6 / 10^4) = 0.609375 x 10^2
Now, let's simplify the decimal:
0.609375 x 10^2 = 6.09375 x 10^1
So the quotient is 6.09375 x 10^1.
To add 3.2x10^4 and 1.95x10^6, you need to make sure that the exponents of the powers of 10 are the same. In this case, both numbers are written in scientific notation, so the exponents are already the same (both are 4).
To add the numbers, simply add the coefficients (the numbers before the powers of 10) together:
3.2x10^4 + 1.95x10^6 = (3.2 + 1.95)x10^4 = 5.15x10^4
Therefore, the sum of 3.2x10^4 and 1.95x10^6 is 5.15x10^4.
To subtract 1.95x10^6 from 3.2x10^4, again make sure that the exponents of the powers of 10 are the same. In this case, the exponents are different (4 and 6).
To subtract the numbers, you need to align the decimal points by moving the decimal places, which will change the exponents of the powers of 10.
First, rewrite both numbers in scientific notation with the same exponent:
3.2x10^4 = 0.00032x10^6
Now, subtract the coefficients:
0.00032x10^6 - 1.95x10^6 = (0.00032 - 1.95)x10^6 = -1.94968x10^6
Therefore, the difference when subtracting 1.95x10^6 from 3.2x10^4 is -1.94968x10^6.
To multiply 3.2x10^4 and 1.95x10^6, you need to multiply the coefficients together and add the exponents:
3.2x10^4 x 1.95x10^6 = (3.2 x 1.95)x10^(4 + 6) = 6.24x10^10
Therefore, the product of 3.2x10^4 and 1.95x10^6 is 6.24x10^10.
To divide 1.95x10^6 by 3.2x10^4, you need to divide the coefficients and subtract the exponents:
(1.95 / 3.2)x10^(6 - 4) = 0.609375x10^2
Simplifying, we get:
0.609375x10^2 = 6.09375x10^1 = 60.9375
Therefore, the result of dividing 1.95x10^6 by 3.2x10^4 is 60.9375.