2. Complete the conversions below. Please show your work and include units in your final answer
i. 8.5m = ? mm
ii. 1.236km = ?cm
iii. 400mL = ?L
iv. 25.25cm = ? Tm
v. 1zm = ? Zm
vi. 45.6mol = ? mmol
vii. 8,000,000km = ? nm
viii. 1000cm3 = ? L
ix. 25m3 = ? cL
x. 1.23 x 104 L = ? m3
They are done this way. Note that the conversion factor is placed such that the units you don't want cancel (the m) and the unit you want to keep stays (mm)
i. 8.5 m x (1000 mm/1 m) = ? mm
iii. 400 mL x (1 L/1000 mL) = ? L
(mL cancels because you don't want that. The L stays so it goes on top).
vii. 8E6 km x (1 000 m/1 km) x (1E9 nm/1 m) = ? nm
You work on the others.
To convert between different units, we need to use conversion factors. A conversion factor is a fraction that represents the relationship between two different units.
i. To convert from meters (m) to millimeters (mm):
1 meter = 1000 millimeters.
Therefore, to convert 8.5 meters to millimeters, we multiply by the conversion factor:
8.5 m * 1000 mm/1 m = 8500 mm
ii. To convert from kilometers (km) to centimeters (cm):
1 kilometer = 100,000 centimeters.
Therefore, to convert 1.236 kilometers to centimeters, we multiply by the conversion factor:
1.236 km * 100,000 cm/1 km = 123,600 cm
iii. To convert from milliliters (mL) to liters (L):
1 liter = 1000 milliliters.
Therefore, to convert 400 milliliters to liters, we divide by the conversion factor:
400 mL / 1000 mL/1 L = 0.4 L
iv. To convert from centimeters (cm) to terameters (Tm):
1 centimeter = 1 x 10^-13 terameters.
Therefore, to convert 25.25 centimeters to terameters, we multiply by the conversion factor:
25.25 cm * 1 Tm/1 x 10^-13 cm = 2.525 x 10^-12 Tm
v. To convert from zeptometers (zm) to zettameters (Zm):
1 zeptometer = 1 x 10^-21 zettameters.
Therefore, to convert 1 zeptometer to zettameters, we multiply by the conversion factor:
1 zm * 1 Zm/1 x 10^-21 zm = 1 x 10^-21 Zm
vi. To convert from moles (mol) to millimoles (mmol):
1 mole = 1000 millimoles.
Therefore, to convert 45.6 moles to millimoles, we multiply by the conversion factor:
45.6 mol * 1000 mmol/1 mol = 45600 mmol
vii. To convert from kilometers (km) to nanometers (nm):
1 kilometer = 1 x 10^12 nanometers.
Therefore, to convert 8,000,000 kilometers to nanometers, we multiply by the conversion factor:
8,000,000 km * 1 x 10^12 nm/1 km = 8 x 10^18 nm
viii. To convert from cubic centimeters (cm3) to liters (L):
1 liter = 1000 cubic centimeters.
Therefore, to convert 1000 cubic centimeters to liters, we divide by the conversion factor:
1000 cm3 / 1000 cm3/1 L = 1 L
ix. To convert from cubic meters (m3) to centiliters (cL):
1 cubic meter = 1 x 10^5 centiliters.
Therefore, to convert 25 cubic meters to centiliters, we multiply by the conversion factor:
25 m3 * 1 x 10^5 cL/1 m3 = 2.5 x 10^6 cL
x. To convert from liters (L) to cubic meters (m3):
1 liter = 0.001 cubic meters.
Therefore, to convert 1.23 x 10^4 liters to cubic meters, we multiply by the conversion factor:
1.23 x 10^4 L * 0.001 m3/1 L = 12.3 m3