Quantities with different units cannot be added directly.
2255.6 millimeters
Practice makes perfect
We need to find the total distance represented by the given expression.
1 mm + 1 cm + 1 in + 1 ft + 1 yd + 1 m
We want our result to be given in millimeters. Notice that we cannot just add the quantities directly as they are not in the same units. We should first convert them to millimeters. Let's take a look at the equivalences for the given units to millimeters.
Unit
Equivalence
1 centimeter
1 cm = 10 mm
1 inch
1 in = 2.54 cm
1 foot
1 ft = 12 in
1 yard
1 yd = 3 ft
1 meter
1 m = 1000 mm
To do the conversions we will need to find the appropriate conversion factor. Remember that for a conversion factor to work, the units should be set in such a way that they cancel the unwanted units. We will need a conversion factor for each unit which needs to be converted.
Quantity
Conversion
Equivalence
1 cm
1 cm ( 10 mm/1 cm )
10 mm
1 in
1 in ( 2.54 cm/1 in ) ( 10 mm/1 cm )
25.4 mm
1 ft
1 ft ( 12 in/1 ft ) ( 25.4 mm/1 in )
304.8 mm
1yd
1 yd ( 3 ft/1 yd ) ( 304.8 mm/1 ft )
914.4mm
1m
1 m ( 1000 mm/1 m )
1000 mm
Notice that once we found the equivalence between certain units, for example 1 in = 25.4 mm, we could use it in the conversion factor for the next conversion. Now that all the quantities are in millimeters, we can perform the sum to find the result we need.
1 + 10 + 25.4 + 304.8 + 914.4 + 1000 = 2255.6
Hence, the length of the line is 2255.6 millimeters.
