Measurement

Ontario 10 Applied (MFM2P)

Imperial units - Length

Lesson

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 fee*t* , 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 *

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**: 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.

**Do**:

$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**: 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.

**Do**:

$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 |

$12$12 in =

$8$8 in =

$5$5 ft =

$10$10 in =

$24$24 ft

$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):

$100$100 km =

$50$50 km =

$130$130 km =

$300$300 km =

$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