Example: Convert 55 centimeters to meters.
First step: Create a fraction with cm in the denominator and meters in the numerator -- _____m/_____cm.
Second step: Fill in the quantity of each unit so that the numerator equals the denominator. To do this, you must know that 1 meter = 100 centimeters.
You can now create a fraction that is equal to one as follows:
1 m / 100 cm.
Third step: Multiply 55cm by the fraction you just created. You will not change the value of the measurement, you will only manipulate the units.
Example: 55cm x 1m/100cm = 55/100 m = .55 m
You see that the centimeters cancel out and you are left with meters as your units.
Show all work for each question listed.
The following are some helpful equalities:
1 m = 100 cm; 1m = 1000 mm
1000 m = 1 km; 1 km = .62 mi
1 L = 1000 mL
1 g = 1000 mg; 1000 g = 1 kg
When converting units that have an exponent (square feet (ft^2) or cubic meters (m^3)),
you must separate the units into their component parts. So 300 ft^2 becomes 300 ft x 1 ft.
You must then create two conversion fractions to change each of those units to the desired
unit. Example: Let's change 300 ft^2 to square meters (m^2).
Step 1: Identify the relationship between feet and meters -- 1 m = 3.281 ft;
Step 2: Separate the given units into their component parts. Rewrite 300 ft^2
as 300 ft x 1 ft;
Step 3: Create two conversion fractions that will convert each foot to meters. Because feet are
in the numerator of the given value, feet will go in the denominator of our conversion fractions,
in order to cancel the given units. Meters will go in the numerator of the conversion fraction.
The conversion fraction thus looks like this: 1 m / 3.281 ft.
Step 4: Now multiply the given value (as rewritten into two components) by the two conversion fractions:
300 ft x 1 ft x (1 m / 3.281 ft) x (1 m / 3.281 ft) = ___________m^2.
Step 5: Now solve. By taking this step-by-step, you will never make the mistake of dividing
when you should be multiplying, and vice versa. The solution: 330 ft^2 = 300 divided by 3.281, which
answer is then divided again by 3.281, which gives us 27.9 m^2.
After you have tried the homework problems yourself, check your answers at the Measurement Converter web site, an interactive site that allows you to convert units.