Scientific measurements are useful only when the number is paired with a suitable unit.
A length of 12 could mean 12 metres, 12 centimetres or 12 millimetres.
Those measurements describe very different sizes.
In this lesson you will practise choosing sensible units and converting between common metric units used in science.
Goal: choose an appropriate unit for a measurement and convert correctly between common units of length, mass and volume.
Before you start
Review Scientific Measurement and Common Units.
You will need a notebook or worksheet and a pencil.
A measurement needs a number and a unit
Consider:
The pencil is 15.
This is incomplete.
Now compare:
The pencil is 15 cm long.
The second statement tells us both the measured value and the unit.
Choose the unit before you convert
Before doing any calculation, ask:
What quantity am I measuring?
Then choose a unit that matches that quantity and gives a useful sized number.
For example:
- length can be measured in kilometres, metres, centimetres or millimetres
- mass can be measured in kilograms, grams or milligrams
- liquid volume can often be measured in litres or millilitres
- time can be measured in seconds or minutes
- temperature is commonly recorded in degrees Celsius in everyday scientific work
Common units of length
Unit Symbol Useful for kilometre km long distances metre m room sized and human sized lengths centimetre cm small everyday objects millimetre mm very small lengths and thicknessesLength relationships
These exact relationships are especially useful:
1 km = 1000 m
1 m = 100 cm
1 cm = 10 mm
From these relationships we can also see:
1 m = 1000 mm
Why prefixes matter
Metric prefixes tell us how large or small a unit is compared with another related unit.
For the units in this lesson:
Prefix Meaning Example kilo 1000 times the unit 1 km = 1000 m centi one hundredth of the unit 1 cm = 0.01 m milli one thousandth of the unit 1 mm = 0.001 mConvert from a larger unit to a smaller unit
When you express the same measurement using a smaller unit, the numerical value becomes larger.
Example:
3 m = 300 cm
Each metre contains 100 centimetres.
So:
3 × 100 = 300
Convert metres to centimetres
Multiply the number of metres by 100.
Example:
2.5 m = 250 cm
Calculation:
2.5 × 100 = 250
Convert centimetres to millimetres
Each centimetre contains 10 millimetres.
Example:
8 cm = 80 mm
Calculation:
8 × 10 = 80
Convert metres to millimetres
Each metre contains 1000 millimetres.
Example:
1.2 m = 1200 mm
Calculation:
1.2 × 1000 = 1200
Convert kilometres to metres
Each kilometre contains 1000 metres.
Example:
4.5 km = 4500 m
Convert from a smaller unit to a larger unit
When you express the same measurement using a larger unit, the numerical value becomes smaller.
Example:
300 cm = 3 m
There are 100 centimetres in one metre.
So:
300 ÷ 100 = 3
Convert centimetres to metres
Divide by 100.
Example:
250 cm = 2.5 m
Convert millimetres to centimetres
Divide by 10.
Example:
75 mm = 7.5 cm
Convert millimetres to metres
Divide by 1000.
Example:
1600 mm = 1.6 m
Convert metres to kilometres
Divide by 1000.
Example:
3500 m = 3.5 km
A useful size check
Before accepting an answer, ask:
Should the numerical value become larger or smaller?
If you convert metres into centimetres, the unit becomes smaller, so the numerical value should become larger.
If you convert centimetres into metres, the unit becomes larger, so the numerical value should become smaller.
This simple check catches many conversion mistakes.
Common units of mass
Unit Symbol Useful for kilogram kg people, large objects and larger samples gram g smaller everyday objects and samples milligram mg very small massesMass relationships
1 kg = 1000 g
1 g = 1000 mg
Convert kilograms to grams
Multiply by 1000.
Example:
2.4 kg = 2400 g
Convert grams to kilograms
Divide by 1000.
Example:
750 g = 0.75 kg
Convert grams to milligrams
Multiply by 1000.
Example:
3 g = 3000 mg
Convert milligrams to grams
Divide by 1000.
Example:
250 mg = 0.25 g
Do not confuse mass with weight
Mass and weight are related but different scientific quantities.
Kilograms and grams are units of mass.
Weight is a force and is measured in newtons.
In everyday conversation people often use the word weight when referring to mass, but scientific measurements should identify the correct quantity.
Common units of liquid volume
Unit Symbol Useful for litre L larger liquid volumes millilitre mL smaller liquid volumesVolume relationship
1 L = 1000 mL
Convert litres to millilitres
Multiply by 1000.
Example:
1.5 L = 1500 mL
Convert millilitres to litres
Divide by 1000.
Example:
600 mL = 0.6 L
Choose a sensible unit
You could describe a bottle as having a volume of 0.5 L or 500 mL.
Both measurements describe the same volume.
The better choice depends on which form makes the information easiest to understand and compare.
Time units
The second is the SI unit of time.
Minutes are also commonly used for longer everyday intervals.
A useful relationship is:
1 min = 60 s
Convert minutes to seconds
Multiply by 60.
Example:
3 min = 180 s
Convert seconds to minutes
Divide by 60.
Example:
150 s = 2.5 min
Temperature
Temperature is different from length, mass and volume.
Do not try to convert degrees Celsius by simply multiplying or dividing by 10, 100 or 1000.
For this lesson, focus on recording Celsius temperatures correctly rather than converting temperature scales.
For example:
22 °C
Write unit symbols correctly
Scientific unit symbols follow standard conventions.
For example:
- metre uses m
- centimetre uses cm
- millimetre uses mm
- kilometre uses km
- gram uses g
- kilogram uses kg
- milligram uses mg
- litre uses L
- millilitre uses mL
- second uses s
Unit symbols do not become plural
Write:
5 kg
not a symbol with an extra letter added to make it plural.
The symbol remains the same whether the value is one unit or many units.
Leave a space between the number and unit symbol
Write:
15 cm
rather than joining the number and unit symbol together.
The same convention applies to Celsius temperature:
25 °C
Prefixes and unit symbols stay together
The prefix symbol is joined directly to the unit symbol.
For example:
- km
- cm
- mm
- mg
- mL
Do not put a space between the prefix and the unit symbol.
Capital letters matter
Unit symbols are case sensitive.
For example:
m means metre
while:
M is the SI prefix mega
Similarly, litre is commonly represented by the uppercase symbol L.
Conversion method 1: Use the known relationship
Suppose you need to convert 4.2 m to centimetres.
Start with:
1 m = 100 cm
Then calculate:
4.2 × 100 = 420
So:
4.2 m = 420 cm
Conversion method 2: Ask whether to multiply or divide
Use this sequence:
- Identify the starting unit.
- Identify the target unit.
- Decide which unit is larger.
- Write the conversion relationship.
- Multiply or divide.
- Check whether the answer changed in the expected direction.
Worked example 1
Convert 6 km to metres.
Relationship:
1 km = 1000 m
The target unit is smaller, so the numerical value should become larger.
Calculation:
6 × 1000 = 6000
Answer:
6 km = 6000 m
Worked example 2
Convert 420 cm to metres.
Relationship:
100 cm = 1 m
The target unit is larger, so the numerical value should become smaller.
Calculation:
420 ÷ 100 = 4.2
Answer:
420 cm = 4.2 m
Worked example 3
Convert 1.8 kg to grams.
1 kg = 1000 g
1.8 × 1000 = 1800
Answer:
1.8 kg = 1800 g
Worked example 4
Convert 2750 mL to litres.
1000 mL = 1 L
2750 ÷ 1000 = 2.75
Answer:
2750 mL = 2.75 L
Worked example 5
Convert 4.5 g to milligrams.
1 g = 1000 mg
4.5 × 1000 = 4500
Answer:
4.5 g = 4500 mg
Use decimals carefully
Metric conversions often move between whole numbers and decimals.
For example:
250 mL = 0.25 L
The amount did not change.
Only the unit used to express the amount changed.
A conversion does not change the measurement itself
This is a key idea.
Consider:
1.2 m
and:
120 cm
These describe the same length.
Changing units changes the numerical representation, not the physical length.
Common mistake 1: Multiplying in the wrong direction
Suppose a learner writes:
3 m = 0.03 cm
This cannot be correct.
A centimetre is smaller than a metre, so the number of centimetres should be larger than the number of metres.
The correct result is:
3 m = 300 cm
Common mistake 2: Forgetting the unit
An answer such as:
500
is incomplete if the question asks for a measurement.
Write:
500 mL
or whatever unit the calculation requires.
Common mistake 3: Changing both the number and the physical amount
Unit conversion should describe the same physical quantity before and after conversion.
If a bottle contains 2 L, converting the value to 2000 mL does not add more liquid.
Common mistake 4: Mixing unrelated quantities
You cannot convert metres directly into grams.
Metres measure length.
Grams measure mass.
A conversion requires units that describe the same kind of quantity.
Common mistake 5: Treating every conversion as a factor of 1000
Many common metric relationships use 1000, but not all do.
For example:
1 m = 100 cm
and:
1 cm = 10 mm
Always write the actual relationship before calculating.
Practice 1
Which unit is more suitable for the length of a classroom?
Metres are a sensible choice.
Practice 2
Which unit is more suitable for the thickness of a coin?
Millimetres are a sensible choice.
Practice 3
Convert 7 m to centimetres.
7 m = 700 cm
Practice 4
Convert 450 cm to metres.
450 cm = 4.5 m
Practice 5
Convert 2.3 km to metres.
2.3 km = 2300 m
Practice 6
Convert 3500 mm to metres.
3500 mm = 3.5 m
Practice 7
Convert 5 kg to grams.
5 kg = 5000 g
Practice 8
Convert 1250 g to kilograms.
1250 g = 1.25 kg
Practice 9
Convert 6 g to milligrams.
6 g = 6000 mg
Practice 10
Convert 750 mL to litres.
750 mL = 0.75 L
Practice 11
Convert 2.25 L to millilitres.
2.25 L = 2250 mL
Practice 12
Convert 4 min to seconds.
4 min = 240 s
Mixed challenge 1
Which measurement is greater?
1.5 m or 140 cm
Convert to the same unit:
1.5 m = 150 cm
Therefore 1.5 m is greater.
Mixed challenge 2
Which mass is greater?
0.8 kg or 750 g
Convert:
0.8 kg = 800 g
Therefore 0.8 kg is greater.
Mixed challenge 3
A container holds 1.25 L.
How many millilitres is that?
1.25 L = 1250 mL
Mixed challenge 4
A sample has a mass of 3200 mg.
Express the mass in grams.
3200 mg = 3.2 g
Compare measurements by converting first
Measurements are easiest to compare when they use the same unit.
For example, comparing:
75 cm and 0.8 m
is easier after conversion:
0.8 m = 80 cm
Now you can see that 80 cm is greater than 75 cm.
A practical conversion checklist
For every conversion, ask:
- What quantity am I measuring?
- What is the starting unit?
- What is the target unit?
- What exact relationship connects those units?
- Should the numerical value become larger or smaller?
- Should I multiply or divide?
- Did I include the correct unit in my answer?
- Does my final answer make sense?
Final challenge
Convert each measurement.
- 3.4 m to centimetres
- 920 cm to metres
- 1.6 kg to grams
- 450 mg to grams
- 3.5 L to millilitres
- 1800 mL to litres
Answers:
- 340 cm
- 9.2 m
- 1600 g
- 0.45 g
- 3500 mL
- 1.8 L
The main idea
A scientific measurement combines a numerical value with a unit.
Choose a unit that matches the quantity being measured and gives a useful sized number.
Metric prefixes create larger and smaller units using powers of ten.
When converting to a smaller unit, the numerical value usually becomes larger.
When converting to a larger unit, the numerical value usually becomes smaller.
Always use the exact conversion relationship, keep the physical quantity unchanged and include the correct unit in the final answer.
These skills make scientific measurements easier to record, compare and interpret.
Continue learning
Review Scientific Measurement and Common Units whenever you need to revisit measurement quantities and common scientific units.