Applying relationship between units (Unit conversion)

General information

"Apply the relationships between units in the metric system, including the units for measuring different attributes and derived measures." is a part of the Geometry and Measurement area in level 6 of Mathematics and Statistics in the New Zealand curriculum. Sililar to "Measuring at an appropriate level", this is rarely directly assessed in the form of a question, but is a necessary for answering many word questions.

What you need to know

Usually, the "kilo" prefix indicates that the unit is 1000 times the origional unit e.g. one kilometer=1000 meters.

The "mili" prefix indicates that the unit is 1/1000 times the origional unit e.g. one meter=1000 milimeters.

The "centi" prefix indicates that the unit is 1/100 time the origional unit e.g. one meter=100 centimeters.

Keep in mind that if the unit is on more than one dimension e.g. m², the difference between units will also be multiplied. For example, 1cm=10mm, but 1cm²=100mm² (10²=100). This also applies for cubed units, e.g. 1m³=100*100*100=1000000cm³.

The most common units you will use at this level and the conversions for them are listed down below:

Distance:

1km=1000m

1m=10dm=100cm

1cm=10mm

1m=3.28084(3.3)ft

Area:

1km²=1000000m²

1m²=10000cm²

1cm²=100mm²

1ha=10000m²

1ac=4046.86(4000)m²

Time:

1day=24hrs

1hr=60mins

1min=60secs

1sec=1000ms

Volume:

1L=1000mL

Mass:

1t=~1000kg

1kg=1000g

1g=1000mg

1lb=453.592(450)g

Practice Questions

These are some questions we have come up with to help. (the answers can be found in the next section of this page)

1. Convert 535 cm into meters (m).
2. Convert 3.5 m² into centimeters squared (cm²).
3. What is the area of a square with side length 50cm? Give the answer in square meters.
4. Bob studies for 0.5 minutes on Monday and 0.2 minutes on Tuesday. How long does he study for in total? (Give the answer in seconds)

Answers

1: 5.35m

2: 35000cm²

3: 0.25m²

4: Bob studies for 42 seconds in total.

Helpful links

The following are some links you might find helpful, checked so that there is no requirement for registration.

https://www.calculator.net/conversion-calculator.html (convert between units using this)

https://www.wikihow.com/Convert-Units (Great tutorial)

https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-measurement-topic/cc-5th-unit-conversion/e/converting-units (practice questions)