What are the basic units of measurement in the International System of Units (SI)?

The International System of Units (SI) is the most widely used system of measurement. It includes seven basic units: meter (m) for length, kilogram (kg) for mass, second (s) for time, ampere (A) for electric current, kelvin (K) for temperature, mole (mol) for amount of substance, and candela (cd) for luminous intensity. These units form the foundation for all other derived units in the SI system.

How do you convert between different units of measurement?

Converting between different units of measurement involves multiplying or dividing by conversion factors. For example, to convert meters to centimeters, multiply by 100 because there are 100 centimeters in a meter. It's important to understand the relationship between units to apply the correct conversion factor. In the IB MYP Mathematics curriculum, students learn to use conversion tables and dimensional analysis to perform these conversions accurately.

Why is it important to use standardized units of measurement in mathematics?

Using standardized units of measurement ensures consistency and accuracy in communication and calculations. It allows people from different regions and disciplines to understand and compare measurements without confusion. In the context of IB MYP Mathematics, standardized units help students develop a clear understanding of quantities and their relationships, which is essential for solving real-world problems.

What is the difference between metric and imperial units of measurement?

Metric units, part of the International System of Units (SI), are based on powers of ten, making them easy to convert. Examples include meters, liters, and grams. Imperial units, used primarily in the United States, include feet, gallons, and pounds. The IB MYP Mathematics curriculum emphasizes understanding both systems, as students may encounter both in various contexts, and learning to convert between them is a valuable skill.

How are units of measurement used in scientific notation?

In scientific notation, units of measurement are used to express very large or very small numbers in a concise form. This involves writing numbers as a product of a coefficient and a power of ten, along with the appropriate unit. For example, the speed of light can be expressed as 3.00 x 10^8 meters per second (m/s). This method is particularly useful in IB MYP Mathematics for simplifying calculations and clearly communicating measurements in scientific and engineering contexts.

Why is "Converting $\text{cm}^2$ to $\text{m}^2$ by dividing by 100." a common mistake in Units of Measurements?

Why it happens: Treating it like a linear conversion. How to avoid it: Square units use the SQUARE of the linear factor. 1\,m^2 = 100^2 = 10\,000\,cm^2. Divide by 10\,000, not 100.

Why is "Computing speed from $\text{km}$ and $\text{s}$ without conversion." a common mistake in Units of Measurements?

Why it happens: Forgetting to check consistency. How to avoid it: Always convert ALL inputs to consistent units before applying the formula.

Why is "Giving a numerical answer without units." a common mistake in Units of Measurements?

Why it happens: Stopping at the calculation. How to avoid it: Always include units. 4 is meaningless; 4\,km/h is a quantity.

NumberIB MYP Maths Extended Level

Units of Measurements

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Short Study Notes — Units of Measurements

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Units of Measurements — IB MYP Mathematics (Extended): SI prefixes and conversions

Every measurement needs a unit. This MYP Mathematics Extended note covers SI prefixes, unit conversions, compound units, and consistency in calculation.

What you’ll learn

Mapped to the IB MYP Mathematics subject guide (2026 onwards).

MYP Mathematics A — Recall SI prefixes and base units.
MYP Mathematics A — Convert between units within a system.
MYP Mathematics C — Use units consistently throughout a calculation.
MYP Mathematics D — Apply units in scientific and engineering contexts.

SI prefixes

Powers of 10 with standard names.

Each SI prefix scales the base unit by a power of 10:

Prefix	Symbol	Factor
giga	G	$10^9$
mega	M	$10^6$
kilo	k	$10^3$
hecto	h	$10^2$
deca	da	$10^1$
(base)	—	$10^0 = 1$
deci	d	$10^{-1}$
centi	c	$10^{-2}$
milli	m	$10^{-3}$
micro	μ	$10^{-6}$
nano	n	$10^{-9}$

The most common ones at MYP level: kilo, centi, milli, micro.

Examples:

$1\,\text{km} = 1000\,\text{m}$ (kilo).
$1\,\text{cm} = 0.01\,\text{m} = 10^{-2}\,\text{m}$ (centi).
$1\,\text{mm} = 0.001\,\text{m} = 10^{-3}\,\text{m}$ (milli).
$1\,\text{μg} = 10^{-6}\,\text{g}$ (micro).

kilo = $10^3$ , centi = $10^{-2}$ , milli = $10^{-3}$ , micro = $10^{-6}$ .
Each prefix multiplies the base unit by its factor.

Converting between units

Multiply by a conversion factor (which equals 1).

The conversion-factor method. To convert from one unit to another, multiply by a fraction that equals 1 (same physical quantity on top and bottom).

Worked example. Convert $5.2\,\text{km}$ to metres.

$5.2\,\text{km} \times \frac{1000\,\text{m}}{1\,\text{km}} = 5200\,\text{m}.$

The fraction $\tfrac{1000\,\text{m}}{1\,\text{km}}$ equals 1 because they're the same quantity. The $\text{km}$ cancels, leaving $\text{m}$ .

Worked example. Convert $250\,\text{cm}^2$ to $\text{m}^2$ .

Watch out: square units don't convert linearly. $1\,\text{m} = 100\,\text{cm}$ so $1\,\text{m}^2 = (100)^2 = 10\,000\,\text{cm}^2$ .

$250\,\text{cm}^2 \times \frac{1\,\text{m}^2}{10\,000\,\text{cm}^2} = 0.025\,\text{m}^2.$

For CUBIC units, the factor is cubed: $1\,\text{m}^3 = 10^6\,\text{cm}^3$ .

Time conversions (non-SI but essential):

$60\,\text{s} = 1\,\text{min}$ .
$3600\,\text{s} = 1\,\text{h}$ .
$86\,400\,\text{s} = 1\,\text{day}$ .

Worked example. Convert $72\,\text{km/h}$ to $\text{m/s}$ .

$72\,\dfrac{\text{km}}{\text{h}} \times \dfrac{1000\,\text{m}}{1\,\text{km}} \times \dfrac{1\,\text{h}}{3600\,\text{s}} = \dfrac{72\,000}{3600} = 20\,\text{m/s}.$

A quick rule: divide km/h by 3.6 to get m/s.

Multiply by a fraction equal to 1 (units on top and bottom).
Square units: square the linear factor.
Cubic units: cube the linear factor.
km/h $\div 3.6$ = m/s.

Compound units

Speed, density, force — combinations of base units.

Compound units combine two or more base units.

Quantity	Formula	Unit
Speed	distance / time	$\text{m/s}$ or $\text{km/h}$
Density	mass / volume	$\text{kg/m}^3$ or $\text{g/cm}^3$
Acceleration	velocity / time	$\text{m/s}^2$
Force	mass × acceleration	$\text{N} = \text{kg·m/s}^2$
Pressure	force / area	$\text{Pa} = \text{N/m}^2$

Strategy for compound-unit problems.

Convert ALL inputs to consistent base units.
Apply the formula.
Check the units of your answer.

Worked example. A car covers $45\,\text{km}$ in $30\,\text{minutes}$ . Find its speed in m/s.

Convert: $45\,\text{km} = 45\,000\,\text{m}$ ; $30\,\text{min} = 1800\,\text{s}$ .
Speed = $\dfrac{45\,000}{1800} = 25\,\text{m/s}$ .

(Or: $45\,\text{km} / 0.5\,\text{h} = 90\,\text{km/h} \div 3.6 = 25\,\text{m/s}$ .)

Worked example. Find the density of a $200\,\text{g}$ object with volume $50\,\text{cm}^3$ .

Density = $\dfrac{200}{50} = 4\,\text{g/cm}^3$ .

If you wanted SI units (kg/m³), convert: $1\,\text{g/cm}^3 = 1000\,\text{kg/m}^3$ , so density = $4000\,\text{kg/m}^3$ .

Compound units = base units multiplied/divided.
Convert to consistent units BEFORE computing.
Always state the unit in the final answer.

How it’s examined

Criterion A: convert between units. Criterion C: state units clearly. Criterion D: real-context measurements with consistent units.

Sources: IB MYP Mathematics subject guide (IBO, official). Last reviewed 2026-05-25.

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Step-by-step worked examples — Units of Measurements

Step-by-step solutions to past-paper-style questions on units of measurements, written exactly the way a tutor would explain them at the board.

1Convert with SI prefix
Getting started• prefix
Question
Convert $3.4\,\text{km}$ to mm.
Step-by-step solution
1. Step 1
  $1\,\text{km} = 10^3\,\text{m}$ and $1\,\text{m} = 10^3\,\text{mm}$ .
2. Step 2
  $3.4\,\text{km} \times 10^3\,\text{m/km} \times 10^3\,\text{mm/m} = 3.4 \times 10^6\,\text{mm}$ .
Answer
$3.4 \times 10^6\,\text{mm}$ (or $3\,400\,000\,\text{mm}$ ).
2Convert area
Building confidence• area
Question
Convert $7\,500\,\text{cm}^2$ to $\text{m}^2$ .
Step-by-step solution
1. Step 1
  $1\,\text{m} = 100\,\text{cm}$ , so $1\,\text{m}^2 = 100^2\,\text{cm}^2 = 10\,000\,\text{cm}^2$ .
2. Step 2
  $7\,500\,\text{cm}^2 \times \dfrac{1\,\text{m}^2}{10\,000\,\text{cm}^2} = 0.75\,\text{m}^2$ .
Answer
$0.75\,\text{m}^2$
3km/h to m/s
Building confidence• speed
Question
Convert $90\,\text{km/h}$ to m/s.
Step-by-step solution
1. Step 1
  Multiply by $\dfrac{1000\,\text{m}}{1\,\text{km}}$ and $\dfrac{1\,\text{h}}{3600\,\text{s}}$ .
2. Step 2
  $90 \times \dfrac{1000}{3600} = \dfrac{90}{3.6} = 25\,\text{m/s}$ .
Answer
$25\,\text{m/s}$
4Find density
Stretch• density
Question
A block of mass $2.4\,\text{kg}$ has volume $300\,\text{cm}^3$ . Find its density in kg/m³.
Step-by-step solution
1. Step 1
  Convert volume: $300\,\text{cm}^3 \times \dfrac{1\,\text{m}^3}{10^6\,\text{cm}^3} = 3 \times 10^{-4}\,\text{m}^3$ .
2. Step 2
  Density = $\dfrac{\text{mass}}{\text{volume}} = \dfrac{2.4}{3 \times 10^{-4}}\,\text{kg/m}^3 = 8000\,\text{kg/m}^3$ .
Answer
$8000\,\text{kg/m}^3$ (about the density of iron).

Key Definitions and Keywords — Units of Measurements

Definitions to memorise and the exact keywords mark schemes credit for units of measurements answers — sharpened from recent examiner reports for the 2026 IB MYP Mathematics (Extended) sitting.

SI unit
Examiner keyword
An internationally agreed standard unit of measurement.
SI prefix
Examiner keyword
A letter (k, m, μ, ...) attached to a unit to scale it by a power of 10.
Compound unit
A unit formed by combining base units (e.g. m/s, kg/m³).

Common Mistakes and Misconceptions — Units of Measurements

The traps other students keep falling into on units of measurements questions — taken from recent IB MYP Mathematics (Extended) examiner reports and mark schemes — and how to avoid them.

✕Converting $\text{cm}^2$ to $\text{m}^2$ by dividing by 100.
Why it happens
Treating it like a linear conversion.
How to avoid it
Square units use the SQUARE of the linear factor. $1\,\text{m}^2 = 100^2 = 10\,000\,\text{cm}^2$ . Divide by $10\,000$ , not 100.
✕Computing speed from $\text{km}$ and $\text{s}$ without conversion.
Why it happens
Forgetting to check consistency.
How to avoid it
Always convert ALL inputs to consistent units before applying the formula.
✕Giving a numerical answer without units.
Why it happens
Stopping at the calculation.
How to avoid it
Always include units. $4$ is meaningless; $4\,\text{km/h}$ is a quantity.

Practice questions

Exam-style questions with step-by-step worked solutions. Try one before checking the method.

Past paper style quiz

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Units of Measurements — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Prefix

Symbol

Factor

giga

10^9

mega

10^6

kilo

10^3

hecto

10^2

deca

10^1

(base)

—

10^0 = 1

deci

10^{-1}

centi

10^{-2}

milli

10^{-3}

micro

10^{-6}

nano

10^{-9}

The conversion-factor method. To convert from one unit to another, multiply by a fraction that equals 1 (same physical quantity on top and bottom).

Worked example. Convert $5.2\,\text{km}$ to metres.

$5.2\,\text{km} \times \frac{1000\,\text{m}}{1\,\text{km}} = 5200\,\text{m}.$

The fraction $\tfrac{1000\,\text{m}}{1\,\text{km}}$ equals 1 because they're the same quantity. The $\text{km}$ cancels, leaving $\text{m}$ .

Worked example. Convert $250\,\text{cm}^2$ to $\text{m}^2$ .

Watch out: square units don't convert linearly. $1\,\text{m} = 100\,\text{cm}$ so $1\,\text{m}^2 = (100)^2 = 10\,000\,\text{cm}^2$ .

$250\,\text{cm}^2 \times \frac{1\,\text{m}^2}{10\,000\,\text{cm}^2} = 0.025\,\text{m}^2.$

For CUBIC units, the factor is cubed: $1\,\text{m}^3 = 10^6\,\text{cm}^3$ .

Time conversions (non-SI but essential):

$60\,\text{s} = 1\,\text{min}$ .
$3600\,\text{s} = 1\,\text{h}$ .
$86\,400\,\text{s} = 1\,\text{day}$ .

Worked example. Convert $72\,\text{km/h}$ to $\text{m/s}$ .

$72\,\dfrac{\text{km}}{\text{h}} \times \dfrac{1000\,\text{m}}{1\,\text{km}} \times \dfrac{1\,\text{h}}{3600\,\text{s}} = \dfrac{72\,000}{3600} = 20\,\text{m/s}.$

A quick rule: divide km/h by 3.6 to get m/s.

Quantity

Formula

Unit

Speed

distance / time

\text{m/s}

\text{km/h}

Density

mass / volume

\text{kg/m}^3

\text{g/cm}^3

Acceleration

velocity / time

\text{m/s}^2

Force

mass × acceleration

\text{N} = \text{kg·m/s}^2

Pressure

force / area

\text{Pa} = \text{N/m}^2

Units of Measurements

Short Study Notes in the form of Slides

Short Study Notes — Units of Measurements

Detailed Notes

What you’ll learn

How it’s examined

1Convert with SI prefix

2Convert area

3km/h to m/s

4Find density

SI unit

SI prefix

Compound unit

✕Converting cm2\text{cm}^2cm2 to m2\text{m}^2m2 by dividing by 100.

✕Computing speed from km\text{km}km and s\text{s}s without conversion.

✕Giving a numerical answer without units.

Practice questions

Past paper style quiz

Assess your understanding

Units of Measurements — frequently asked questions

Units of Measurements

Short Study Notes in the form of Slides

Short Study Notes — Units of Measurements

Detailed Notes

What you’ll learn

How it’s examined

1Convert with SI prefix

2Convert area

3km/h to m/s

4Find density

SI unit

SI prefix

Compound unit

✕Converting cm2\text{cm}^2cm2 to m2\text{m}^2m2 by dividing by 100.

✕Computing speed from km\text{km}km and s\text{s}s without conversion.

✕Giving a numerical answer without units.

Practice questions

Past paper style quiz

Assess your understanding

Units of Measurements — frequently asked questions

✕Converting $\text{cm}^2$ to $\text{m}^2$ by dividing by 100.

✕Computing speed from $\text{km}$ and $\text{s}$ without conversion.

✕Converting $\text{cm}^2$ to $\text{m}^2$ by dividing by 100.

✕Computing speed from $\text{km}$ and $\text{s}$ without conversion.