Absolutely, let's go through each conversion step by step.
1. Convert -100 cm to meters (m):
- We know that 1 cm is equal to 0.01 meters. Therefore, to convert -100 cm to meters, we multiply -100 by 0.01:
[tex]\[
-100 \, \text{cm} \times 0.01 \, \frac{\text{m}}{\text{cm}} = -1.0 \, \text{m}
\][/tex]
- So, [tex]\(-100 \, \text{cm}\)[/tex] is [tex]\(-1.0 \, \text{m}\)[/tex].
2. Convert [tex]\(27^{\circ} C\)[/tex] to Kelvin (K):
- The formula to convert Celsius to Kelvin is [tex]\(K = C + 273.15\)[/tex]:
[tex]\[
27^{\circ} C + 273.15 = 300.15 \, K
\][/tex]
- Thus, [tex]\(27^{\circ} C\)[/tex] is [tex]\(300.15 \, K\)[/tex].
3. Convert 20 decigrams (dg) to milligrams (mg):
- We know that 1 dg is equal to 100 milligrams. So, to convert 20 dg to milligrams, we multiply 20 by 100:
[tex]\[
20 \, \text{dg} \times 100 \, \frac{\text{mg}}{\text{dg}} = 2000 \, \text{mg}
\][/tex]
- Therefore, [tex]\(20 \, \text{dg}\)[/tex] is [tex]\(2000 \, \text{mg}\)[/tex].
4. Convert 3 meters (m) to decimeters (dm):
- We know that 1 meter is equal to 10 decimeters. Thus, to convert 3 meters to decimeters, we multiply 3 by 10:
[tex]\[
3 \, \text{m} \times 10 \, \frac{\text{dm}}{\text{m}} = 30 \, \text{dm}
\][/tex]
- Hence, [tex]\(3 \, \text{m}\)[/tex] is [tex]\(30 \, \text{dm}\)[/tex].
In summary, the results of the conversions are:
- [tex]\(-100 \, \text{cm}\)[/tex] is [tex]\(-1.0 \, \text{m}\)[/tex].
- [tex]\(27^{\circ} C\)[/tex] is [tex]\(300.15 \, K\)[/tex].
- [tex]\(20 \, \text{dg}\)[/tex] is [tex]\(2000 \, \text{mg}\)[/tex].
- [tex]\(3 \, \text{m}\)[/tex] is [tex]\(30 \, \text{dm}\)[/tex].
