evaluate each of the following and express with SI units having an appropriate prefix:
(1) (50mN)(6GN)
(2) (400mm) (0.6MN)^2
(3) 45 MN^3/900Gg
Evaluate each of the following and express with SI units having an appropriate prefix. Show all steps.
(50mN) (6GN) b. (400 mm) (0.6 MN) 2 c. (45 MN) 3 /900 Gg (3)
45 MN/900Gg
1) 3 x 10^4 (N^2)
2)2.4 x 10^11 (mN^2)
3)5 x 10^-2 (N^3/kg)
I am grateful
(50 mN)(6 GN)
yes
Am gratiful
To evaluate each of the expressions and express them in SI units with an appropriate prefix, we'll need to understand the prefixes used in the International System of Units (SI).
Here are the commonly used SI prefixes:
- Kilo (k): 10^3
- Mega (M): 10^6
- Giga (G): 10^9
- Milli (m): 10^-3
- Micro (μ): 10^-6
- Nano (n): 10^-9
Now, let's evaluate each of the expressions:
(1) (50mN)(6GN):
To multiply these values, we need to combine the numerical values and the units separately.
50mN = 50 x 10^-3 N (since milli = 10^-3)
6GN = 6 x 10^9 N (since giga = 10^9)
To multiply the numerical values: (50 x 10^-3) x (6 x 10^9) = 300 x 10^6 = 3 x 10^8
To combine the units: N x N = N^2
Therefore, the expression (50mN)(6GN) evaluates to 3 x 10^8 N^2.
(2) (400mm)(0.6MN)^2:
Similar to the previous expression, let's convert the values to SI units.
400mm = 400 x 10^-3 m (since milli = 10^-3)
0.6MN = 0.6 x 10^6 N (since mega = 10^6)
To multiply the numerical values: (400 x 10^-3) x (0.6 x 10^6)^2 = (400 x 0.6^2) x (10^-3 x 10^6)^2 = 0.864 x 10^-3 x 10^12 = 0.864 x 10^9
To combine the units: m x N^2 = mN^2
Therefore, the expression (400mm)(0.6MN)^2 evaluates to 0.864 x 10^9 mN^2.
(3) 45 MN^3/900 Gg:
Let's convert the values to SI units.
45 MN^3 = 45 x 10^6 N x (N^2) (since mega = 10^6)
900 Gg = 900 x 10^9 g = 900 x 10^6 kg (since giga = 10^9)
To divide the numerical values: (45 x 10^6) / (900 x 10^6) = 45 / 900 = 0.05
To combine the units: N x kg = Nkg
Therefore, the expression 45 MN^3/900 Gg evaluates to 0.05 Nkg.
In conclusion, the evaluated expressions expressed in SI units with appropriate prefixes are:
(1) (50mN)(6GN) evaluates to 3 x 10^8 N^2.
(2) (400mm)(0.6MN)^2 evaluates to 0.864 x 10^9 mN^2.
(3) 45 MN^3/900 Gg evaluates to 0.05 Nkg.