Ontario 10 Applied (MFM2P)
topic badge
Imperial units - Length

Everything in math that relates to the ‘real world’ has units. If there is a point to it there are units attached to it. Sometimes the units could be people, buildings, cars, food, shapes.

Basically units relate to the WHAT in mathematics, and you should ALWAYS use them. This helps to convey a clear message to the reader WHAT it is that you are talking about. 

There are some units we need to know about formally, and how to convert between them. 

LENGTH/DISTANCE -->  inches, feet, yards, miles 

AREA  --> square feet , square yards,  acres, square miles

VOLUME --> cubic inches, cubic feet, cubic yards

CAPACITY -->  fluid ounce, pint, gallon

WEIGHT (actually called MASS)  -->  ounce, pound, stone, hundredweight, ton

TIME -->  s, mins, hrs, days, weeks, months, years 

Units of Length

Distances are usually measured in one of the following units: 

  • inch (in or " 
  • foot (ft or ' 
  • yard (yd
  • mile 

You would be used to most of these through previous experiences in measuring heights, lengths, drawing with your rulers, measuring objects or distances between places. 

$1$1 feet = $12$12 inches
$1$1 yard = $3$3 feet = $36$36 inches 
$1$1 mile = $1760$1760 yards = $5280$5280 feet = $63360$63360 inches

To move from larger length units to smaller length units multiply each step.

To move from smaller length units to larger length units divide each step.


question 1

Question: Change $6.4$6.4 miles into feet. 

Think: Think about the steps needed to move from miles to feet.  (miles-> yards-> feet) and identify the multiplicative amounts for each step.  I suggest moving through each step one part at a time.


$6.4$6.4 miles $=$= $6.4\times1760$6.4×1760 yards
  $=$= $11264$11264 yards
  $=$= $11264\times3$11264×3 feet
  $=$= $33792$33792 feet

It really doesn't matter if you think about it like I did, or if you do something different.  What is important is to keep track of your steps.

Here is another

question 2

Question: Convert $148896$148896 inches into yards

Think: Think about the steps needed to move from inches to yards.  (inches -> feet -> yards) and identify the division amounts for each step. 


$1498896$1498896 $=$= $148896\div12$148896÷​12 (into feet)
  $=$= $12408\div3$12408÷​3 (into yards)
  $=$= $4136$4136 yards 

Using the conversions in the given table, convert these lengths from imperial to metric units.

Conversion Table
$1$1 in $=$= $2.5$2.5 cm
$1$1 ft $=$= $30$30 cm
  1. $12$12 in =

  2. $8$8 in =

  3. $5$5 ft =

  4. $10$10 in =

  5. $24$24 ft

  6. $36$36 in =


Using the approximate conversion 5 miles = 8 km, convert these lengths from km to miles (writing your answer correct to $2$2 decimal places where necessary):

  1. $100$100 km =

  2. $50$50 km =

  3. $130$130 km =

  4. $300$300 km =

  5. $10$10 km =



Perform everyday conversions between the imperial system and the metric system and within these systems, as necessary to solve problems involving measurement

What is Mathspace

About Mathspace