Ontario 09 Academic (MPM1D)

Units of capacity

Lesson

As we have been learning, everything in math that relates to the ‘real world’ has units. If an amount represents a real life quantity, it has units attached to it. The units that we use depend on what we are measuring.

There are some units we need to be familiar with, and know how to convert between.

LENGTH/DISTANCE | mm, cm, m, km |
---|---|

AREA | mm^{2}, cm^{2}, m^{2}, km^{2} |

VOLUME | mm^{3}, cm^{3}, m^{3}, km^{3} |

CAPACITY | mL, L, kL, ML |

WEIGHT (MASS) | mg, g, kg, metric tonne |

TIME | sec, mins, hrs, days, weeks, months, years |

Capacity is the amount of liquid that a container can hold. Capacity is usually measured using one of the following units:

- millilitres (
*mL*) - litres (
*L*) - kilolitres (
*kL*) - megalitres (ML)

You would be used to most of these through previous experiences in the size of your milk container, measuring ingredients when cooking, measuring medicines or even in science experiments you may have done at school.

$1$1 *L *= $1000$1000 *mL*

$1$1 *kL *= $1000$1000 *L* = $1000000$1000000 *mL *($1000\times1000$1000×1000)

$1$1 *ML* = $1000$1000 *kL* = $1000000$1000000 *L* = $1000000000$1000000000 *mL* Thats about 200 million full teaspoons!

To move from larger capacity units to smaller capacity units we multiply at each step.

To move from smaller capacity units to larger capacity units we divide at each step.

Do you see some patterns when looking at changing units of capacity? For example, notice that there is a factor of 1000 between each step.

You see here that we also use the prefixes of milli and kilo again. Remember that the prefix **milli **means $\frac{1}{1000}$11000 th of something. So we can see here that a *millilitre *is $\frac{1}{1000}$11000th of a *litre*, which means that there are $1000$1000 *mL* in $1$1 *litre*. Also the prefix **kilo**means $1000$1000 lots of something, so a *kilolitre *is $1000$1000 *litres. *

**Question**: Change $6.732$6.732kL into mL.

**Think**: Think about the steps needed to move from kL to mL, (kL -> L -> mL) and identify the multiplication amounts for each step. I suggest moving through one step at a time.

**Do**:

First convert to litres: $6.732\times1000=6732$6.732×1000=6732 L

Then convert to millilitres: $6732\times1000=6732000$6732×1000=6732000 mL

It really doesn't matter if you think about it like I did, or if you do it differently. What is important is to keep track of your steps. See how my units changed at each calculation.

Here is another:

**Question**: Convert $468296$468296 mL into litres

**Think**: Think about the steps needed to move from ml to litres, (mL -> L ) and identify the division amounts for each step.

**Do**:

$468296\div1000$468296÷1000 | $=$= | $468.296$468.296 L |

Convert $3\frac{4}{5}$345 litres to millilitres.

$3\frac{4}{5}$345 litres = $\editable{}$ millilitres

Convert each of the following volumes to the indicated unit:

$2000$2000 mL = $\editable{}$ L

$5$5 kL = $\editable{}$ L

$240$240 mL = $\editable{}$ L

$0.4$0.4 L= $\editable{}$ mL

How many $150$150 millilitre jugs of soda water will be needed to fill a $2.4$2.4 litre container?

Solve problems involving the surface areas and volumes of prisms, pyramids, cylinders, cones, and spheres, including composite figures