Measurement

NZ Level 6 (NZC) Level 1 (NCEA)

Units of Volume and Capacity

Lesson

As we have been learning, everything in maths 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 |

It is probably worthwhile to remind ourselves of the units that are often used for calculations involving volume.

Units of Volume

**cubic millimetres = mm ^{3}**

(picture a cube with side lengths of 1 mm each - pretty small this one!)

**cubic centimetres = cm ^{3}**

(picture a cube with side lengths of 1 cm each - about the size of a dice)

**cubic metres = m ^{3} **

(picture a cube with side lengths of 1 m each - what could be this big?)

AND to convert to **capacity - 1cm ^{3} = 1mL**

Apply the relationships between units in the metric system, including the units for measuring different attributes and derived measures

Apply measurement in solving problems