Although I do very well in chemistry I never really understood converting units.
Perform each of the following conversions.
A. 8.43cm to millimeters
B. 2.41x10^2cm to meters
C. 294.5nm to cm
D. 1.445x10^4m to kilometers
E. 235.3m to millimeters
F. 903.3nm to micrometers
A factor converts any unit to any other unit. The factor used depends upon which unit you have and which unit you want.
For example. A.
There are 10 mm to 1 cm so the conversion factor is 10mm/1cm or you can write it the other way as 1 cm/10mm.
8.43 cm x factor = ? mm
Now we decide which of the factors to use.
So we can write it one of two ways.
8.43 cm x (10mm/1 cm) = ?. You note if we write it this way the cm units cancel (those are the units we don't want to keep) and the only unit left is mm is the unit we want to keep.
The other way of writing it is
8.43cm x (1 cm/10mm) = ?
Note that this way no unit cancels and we end up with an answer of ? cm^2/mm which is not what we want.
So of the two ways to write the factor you always use the one in which the unit you are changing from gets canceled and the unit you want to convert to is the only unit left.
Converting units can be tricky at first, but with practice, it becomes easier. The key to conversion is understanding the relationships between different units. I'll explain the process for each of the given conversions.
A. Converting 8.43cm to millimeters:
To convert centimeters to millimeters, you need to multiply by a conversion factor. Since there are 10 millimeters in one centimeter, the conversion factor is 10. Therefore, you can multiply 8.43cm by 10 to get the equivalent value in millimeters:
8.43cm * 10 = 84.3mm
B. Converting 2.41x10^2cm to meters:
To convert centimeters to meters, you need to divide by a conversion factor. Since there are 100 centimeters in one meter, the conversion factor is 1/100 or 0.01. Therefore, divide 2.41x10^2cm by 0.01 to get the equivalent value in meters:
2.41x10^2cm / 0.01 = 2.41x10^2m (in scientific notation)
C. Converting 294.5nm to cm:
To convert nanometers to centimeters, you need to divide by a conversion factor. Since there are 10,000,000 nanometers in one centimeter, the conversion factor is 1/10,000,000 or 1x10^(-8). Therefore, divide 294.5nm by 1x10^(-8) to get the equivalent value in centimeters:
294.5nm / (1x10^(-8)) = 2.945cm
D. Converting 1.445x10^4m to kilometers:
To convert meters to kilometers, you need to divide by a conversion factor. Since there are 1000 meters in one kilometer, the conversion factor is 1/1000 or 0.001. Therefore, divide 1.445x10^4m by 0.001 to get the equivalent value in kilometers:
1.445x10^4m / 0.001 = 1.445x10^1km (in scientific notation)
E. Converting 235.3m to millimeters:
To convert meters to millimeters, you need to multiply by a conversion factor. Since there are 1000 millimeters in one meter, the conversion factor is 1000. Therefore, you can multiply 235.3m by 1000 to get the equivalent value in millimeters:
235.3m * 1000 = 235300mm
F. Converting 903.3nm to micrometers:
To convert nanometers to micrometers, you need to divide by a conversion factor. Since there are 1000 nanometers in one micrometer, the conversion factor is 1/1000 or 0.001. Therefore, divide 903.3nm by 0.001 to get the equivalent value in micrometers:
903.3nm / 0.001 = 903.3 micrometers (in µm)