use 3.2x104 and 1.95 x 106 for steps a,b,c,d. Answers MUST be in correct scientific notation.
Add 3.2 x 104 and 1.95 x 106
Subtract 1.95 x 106 and 3.2 x 104
Multiply 3.2 x 104 and 1.95 x 106
Divide 1.95 x 106 and 3.2 x 104
a) Adding 3.2 x 104 and 1.95 x 106:
(3.2 x 104) + (1.95 x 106) = 19.5 x 105 + 3.2 x 104
= 19.5 x 105 + 0.32 x 106
= (19.5 + 0.32) x 105
= 19.82 x 105
In scientific notation: 1.982 x 106
b) Subtracting 3.2 x 104 from 1.95 x 106:
(1.95 x 106) - (3.2 x 104) = 19.5 x 105 - 0.32 x 105
= (19.5 - 0.32) x 105
= 19.18 x 105
In scientific notation: 1.918 x 106
c) Multiplying 3.2 x 104 and 1.95 x 106:
(3.2 x 104) x (1.95 x 106) = (3.2 x 1.95) x (104 x 106)
= 6.24 x 1010
In scientific notation: 6.24 x 1010
d) Dividing 1.95 x 106 by 3.2 x 104:
(1.95 x 106) / (3.2 x 104) = (1.95 / 3.2) x (106 / 104)
≈ 0.609 x 102
In scientific notation: 6.09 x 101
a) Adding 3.2 x 10^4 and 1.95 x 10^6:
To add these numbers, we need to align the decimal places. Then add the coefficients while keeping the same base (10) and adjust the exponent if needed.
3.2 x 10^4 + 1.95 x 10^6 = 0.32 x 10^5 + 1.95 x 10^6 = 0.32 x 10^5 + 19.5 x 10^5
Since the bases (10) are the same, we can add the coefficients:
0.32 x 10^5 + 19.5 x 10^5 = 19.82 x 10^5
To rewrite this in scientific notation, we need to adjust the coefficient and the exponent:
19.82 x 10^5 = 1.982 x 10^6 (Answer in scientific notation)
b) Subtracting 1.95 x 10^6 and 3.2 x 10^4:
Similar to addition, we need to align the decimal places. Then subtract the coefficients while keeping the same base (10) and adjust the exponent if needed.
1.95 x 10^6 - 3.2 x 10^4 = 1.95 x 10^6 - 0.032 x 10^6
Since the bases (10) are the same, we can subtract the coefficients:
1.95 x 10^6 - 0.032 x 10^6 = 1.918 x 10^6
The answer in scientific notation is 1.918 x 10^6.
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 1.95) x (10^4 x 10^6) = 6.24 x 10^(4+6)
We can simplify the exponent:
6.24 x 10^(4+6) = 6.24 x 10^10 (Answer in scientific notation)
d) Dividing 1.95 x 10^6 and 3.2 x 10^4:
To divide these numbers, we divide the coefficients and subtract the exponents:
(1.95 ÷ 3.2) x (10^6 ÷ 10^4) = 0.609375 x 10^(6-4)
We can simplify the exponent:
0.609375 x 10^(6-4) = 0.609375 x 10^2
Since the coefficient is not in scientific notation, we can rewrite it as:
0.609375 x 100 = 60.9375
The answer can be written in scientific notation as:
60.9375 = 6.09375 x 10^1 (Answer in scientific notation)
To add 3.2 x 10^4 and 1.95 x 10^6, you can simply add the numbers together, but keep the powers of 10 the same. The result will be expressed in scientific notation.
Step a: 3.2 x 10^4 + 1.95 x 10^6 = (3.2 + 1.95) x 10^6
Step b: 3.2 + 1.95 = 5.15
Step c: 5.15 x 10^6
So, the sum of 3.2 x 10^4 and 1.95 x 10^6 is 5.15 x 10^6.
To subtract 1.95 x 10^6 from 3.2 x 10^4, you can again subtract the numbers and keep the powers of 10 the same.
Step a: 1.95 x 10^6 - 3.2 x 10^4 = (1.95 - 0.032) x 10^6
Step b: 1.95 - 0.032 = 1.918
Step c: 1.918 x 10^6
So, the difference between 1.95 x 10^6 and 3.2 x 10^4 is 1.918 x 10^6.
To multiply 3.2 x 10^4 and 1.95 x 10^6, you can multiply the numbers and add the exponents of 10.
Step a: (3.2 x 1.95) x (10^4 x 10^6)
Step b: 3.2 x 1.95 = 6.24
Step c: 10^4 x 10^6 = 10^(4+6) = 10^10
Step d: 6.24 x 10^10
So, the product of 3.2 x 10^4 and 1.95 x 10^6 is 6.24 x 10^10.
To divide 1.95 x 10^6 by 3.2 x 10^4, you can divide the numbers and subtract the exponents of 10.
Step a: (1.95 ÷ 3.2) x (10^6 ÷ 10^4)
Step b: 1.95 ÷ 3.2 = 0.609375
Step c: 10^6 ÷ 10^4 = 10^(6-4) = 10^2
Step d: 0.609375 x 10^2
So, the quotient of 1.95 x 10^6 divided by 3.2 x 10^4 is 0.609375 x 10^2.