3.1.4 Unit conversions
Converting between units of length can be done using conversion factors.
Here are the steps to convert between two units of length:
Step 1: Determine the conversion factor
Find the conversion factor between the two units of length.
The conversion factor tells you how many of one unit of length are equal to one unit of the other length.
For example, there are \( 12 \) inches in \( 1 \) foot, so the conversion factor from feet to inches is \( 12 \).
Step 2: Write out the conversion equation
Write out the conversion equation using the conversion factor.
For example, to convert \( 3 \) feet to inches, you would use the equation:
\( 3 feet \times\frac{12 inches}{1 foot}= 36 inches \)
Step 3: Cancel out units
Cancel out the units that are the same on the top and bottom of the conversion factor.
For example, in the conversion factor from feet to inches, the “feet” unit is on top and bottom, so it can be canceled out.
Step 4: Solve the equation
Solve the equation to find the answer in the desired units.
In the example above, the answer is \( 36 \) inches.
Here are some common conversion factors for length:
\( 1 \ inch \ (in)= 2.54 \ centimeters \ (cm) \)
\( 1 \ foot \ (ft)= 0.3048 \ meters \ (m) \)
\( 1 \ centimeter \ (cm)=10 \ millimeters \ (mm) \)
\( 1 \ meter \ (m)=100 \ centimeters \ (cm) \)
\( 1 \ kilometer \ (km)=1000 \ meters \ (m) \)
\( 1 \ mile = 1.609 kilometers \ (km) \)
Tip:
Always double check your work and use the appropriate number of significant figures in your answer.
Converting between units of mass:
To convert between units of mass, follow these steps:
Step 1: Determine the conversion factor
Find the conversion factor between the two units of mass.
The conversion factor tells you how many of one unit of mass are equal to one unit of the other mass.
For example, there are \( 1000 \) grams in \( 1 \)kilogram , so the conversion factor from kilograms to grams is \( 1000 \).
Step 2: Write out the conversion equation
Write out the conversion equation using the conversion factor.
For example, to convert \( 3 \) kilograms to grams, you would use the equation:
\( 3 kilograms \times \frac {1000 grams}{1 kilogram }=3000 grams \)
Step 3: Cancel out units
Cancel out the units that are the same on the top and bottom of the conversion factor.
For example, in the conversion factor from kilograms to grams, the “kilogram” unit is on top and bottom, so it can be canceled out.
Step 4: Solve the equation
Solve the equation to find the answer in the desired units.
In the example above, the answer is \( 3000 \) grams.
Here are some common conversion factors for mass:
\( 1 \ gram \ (g)=1000 \ milligram \ (mg) \)
\( 1 \ kilogram \ (kg)=1000 \ gram \ (g) \)
\( 1 \ gram \ (g)= 0.001 \ kilograms \ (kg) \)
\( 1 \ tonne=1000 \ gram \ (g) \)
\( 1 \ pound \ (lb)= 0.453592 \ kilograms \ kg \)
By using the same technique you can convert between the following units
Units of volume:
Converting between squared units
Converting between cubic units
Test yourself
Question 1:
Change \( 457000 cm^2 \) into \( m^2 \).
[1]
Question 2:
The lake behind a dam has an area of \( 55 \) hectares.
When the gates in the dam are open, water flows out at a rate of \( 75000 \) liters per second.
Show that \( 90 \) million liters of water flows out in \( 20 \) minutes.
[1]
Beneath the surface, the lake has vertical sides.
Calculate the drop in the water level of the lake when the gates are open for \( 20 \) minutes.
Give your answer in centimeters.
\( [1 \ hectare=10^4 \ m^2 , \ 1000 \ liters=1 \ m^3] \)
[3]
Question 3:
Change \( 90 kmh^{-1} \) to \( ms^{-1} \).
[2]
Question 4:
Complete each statement.
A quadrilateral with only pair of parallel sides is called a . . . . . . . . .
[1]
An angle greater than \( 90° \) but less than \( 180° \) is called . . . . . .. . . . .
[1]
Question 5:
Write down the order of rotational symmetry of the diagram.
[1]