Top Rated by Parents/Students Nationwide

Unit Conversions

Converting Units

How do I convert between units for lengths?

  • For metric units, conversion can be done by simply multiplying or dividing by powers of 10
  • You need to know the basic conversions
    • 1 cm = 10 mm
    • 1 m = 100 cm
    • 1 km = 1000 m
  • To decide whether to multiply or divide you need to ask yourselves does the number of units increase or decrease
    • e.g. The number of mm is 10 times bigger than the number of cm so mm = cm × 10
  • You can do the conversion in stages
    • First convert kilometres into metres then metres into centimetres
  • If you are given an imperial conversion (such as miles to kilometres) then you can use ratios to help with the conversions
    • There are 5 miles in 8 kilometres so to find how many miles are in 13 kilometres you would solve  5 space colon space 8 equals x space colon space 13

How do I convert units for mass?

  • For metric units, conversion can be done by simply multiplying or dividing by powers of 10
  • You need to know the basic conversions
    • 1 g = 1000 mg
    • 1 kg = 1000 g
    • 1 tonne = 1000 kg
  • If you are given an imperial conversion (such as pounds to kilograms) then you can use ratios to help with the conversions
    • e.g. There are 2.2 pounds in 1 kilogram so to find how many kilograms are in 10 pounds you would solve  2.2 ∶ 1 equals 10 ∶ x

How do I convert units for volume/capacity?

  • For metric units, conversion can be done by simply multiplying or dividing by powers of 10
  • You need to know the basic conversions
    • 1 l = 1000 ml
    • 1 cl = 10 ml
    • 1 ml = 1 cm 3
  • If you are given an imperial conversion (such as pints to litres) then you can use ratios to help with the conversions
    • e.g. There are 1.75 pints in 1 litre so to find how many litres are in 5 pints you would solve  1.75 ∶ 1 equals 5 ∶ x

Worked example

Convert

a)

54 cm to mm,

1 cm = 10 mm


54 cm = (54 × 10) mm = 540 mm


540 mm

b)

12 300 cm to km,

First convert from cm to m.
100 cm = 1 m


12 300 cm = (12 300 ÷ 100) m = 123 m



Now convert from m to km.

1000 m = 1 km





123 m = (123 ÷ 1000) km = 0.123 km







0.123 km




c)

485 g to kg.

1000 g = 1 kg

450 g = (450 ÷ 1000) kg


0.45 kg

Squared & Cubic Units

How do I convert between squared units?

  • Converting squared units (usually used for areas) is slightly trickier
  • You need to remember to square the conversion rates
    • This is because area is 2D
    • The fact the units have a “squared” on them will help you remember
  • You need to be able to use the basic conversions
    • 1 cm 2 = 10 2 mm 2 = 100 mm 2
    • 1 m 2 = 100 2 cm 2 = 10 000 cm 2
    • 1 km 2 = 1000 2 m 2 = 1 000 000 m 2
  • There are also less common conversions
    • 1 hectare (ha) = 10 000 m 2
  • If you are given an imperial conversion (such as miles to kilometres) for lengths:
    • Write the conversion as a ratio
      • e.g.  Miles to kilometres is 5 : 8
    • Square the numbers to get the ratio for the conversion of the units for area
      • e.g.  Miles 2 to kilometres 2 is 25 : 64

How do I convert between cubed units?

  • You need to cube the normal conversion rates
    • This is because volume is 3D
    • The fact the units have a “cubed” on them will help you remember
  • You need to be able to use the basic conversions
    • 1 cm 3 = 10 3 mm 3 = 1000 mm 3
    • 1 m 3 = 100 3 cm 3 = 1 000 000 cm 3
    • 1 km 3 = 1000 3 m 3 = 1 000 000 000 m 3
  • If you are given an imperial conversion (such as miles to kilometres) for lengths:
    • Write the conversion as a ratio
      • e.g.  Miles to kilometres is 5 : 8
    • Cube the numbers to get the ratio for the conversion of the units for volume
      • e.g.  Miles 3 to kilometres 3 is 125 : 512

Worked example

Convert

a)

8254 mm to cm 2,

10 mm = 1 cm

100 mm 2 = 1 cm 2


8254 mm 2 = (8254 ÷ 100) cm 2 = 82.54 cm 2




82.54 cm 2
  


b)

2.54 m 3 to cm 3.

1 m = 100 cm

1 m 3 = 1 000 000 cm 3

2.54 m

3

= (2.54 × 1 000 000) cm

3 = 2 540 000 cm 3


2 540 000 cm 3

Number Toolkit
  • Mathematical Operations
  • Negative Numbers
  • Money Calculations
  • Number Operations
  • Related Calculations
  • Counting Principles
Prime Factors, HCF & LCM
  • Types of Number
  • Prime Factor Decomposition
  • HCF & LCM
Powers, Roots & Standard Form
  • Powers, Roots & Indices
  • Standard Form
Fractions
  • Basic Fractions
  • Operations with Fractions
Percentages
  • Basic Percentages
  • Working with Percentages
Simple & Compound Interest, Growth & Decay
  • Interest & Depreciation
  • Exponential Growth & Decay
Fractions, Decimals & Percentages
  • Converting between FDP
  • Converting between FDP
Rounding, Estimation & Bounds
  • Rounding & Estimation
  • Bounds
Surds
  • Simplifying Surds
  • Rationalising Denominators
Using a Calculator
  • Using a Calculator
Algebra Toolkit
  • Algebraic Notation & Vocabulary
  • Algebra Basics
Algebraic Roots & Indices
  • Algebraic Roots & Indices
Expanding Brackets
  • Expanding Single Brackets
  • Expanding Multiple Brackets
Factorising
  • Factorising
  • Factorising Quadratics
  • Quadratics Factorising Methods
Completing the Square
  • Completing the Square
Rearranging Formulae
  • Rearranging Formulae
Algebraic Proof
  • Algebraic Proof
Linear Equations
  • Solving Linear Equations
Solving Quadratic Equations
  • Solving Quadratic Equations
  • Quadratic Equation Methods
Simultaneous Equationsr
  • Simultaneous Equations
Iteration
  • Iteration
Forming & Solving Equations
  • Forming Equations
  • Equations & Problem Solving
Functions
  • Functions Toolkit
  • Composite & Inverse Functions
Coordinate Geometrys
  • Coordinates
  • Coordinate Geometry
Linear Graphs y = mx + c
  • Straight Line Graphs (y = mx + c)
  • Parallel & Perpendicular Lines
Graphs of Functions
  • Types of Graphs
  • Graphical Solutions
  • Trig Graphs
Equation of a Circle
  • Equation of a Circle
  • Equation of a Tangents
Estimating Gradients & Areas under Graphs
  • Finding Gradients of Tangents
  • Finding Areas under Graphs
Real-Life Graphs
  • Distance-Time & Speed-Time Graphs
  • Conversion Graphs
  • Rates of Change of Graphs
Solving Inequalities
  • Solving Linear Inequalities
  • Conversion Graphs
  • Solving Quadratic Inequalities
Graphing Inequalities
  • Graphing Inequalities
Transformations of Graphs
  • Reflections of Graphs
Sequences
  • Introduction to Sequences
  • Types of Sequences
  • Linear Sequences
  • Quadratic Sequences
Ratio Toolkit
  • Simple Ratio
  • Working with Proportion
Ratio Problem Solving
Direct & Inverse Proportions
  • Direct & Inverse Proportion
Standard & Compound Units
Exchange Rates & Best Buys
  • Exchange Rates & Best Buys
Geometry Toolkit
  • Symmetry
  • 2D & 3D Shapes
  • Plans & Elevations
Angles in Polygons & Parallel Lines
  • Basic Angle Properties
  • Angles in Polygons
  • Angles in Parallel Lines
Bearings, Scale Drawing, Constructions & Loci
  • Bearings
  • Scale & Maps
  • Constructing Triangles
  • Constructions & Loci
Circle Theorems
  • Angles at Centre & Semicircles
  • Chords & Tangents
  • Cyclic Quadrilaterals
  • Segment Theorems
  • Circle Theorem Proofs
Area & Perimeter
  • Area & Perimeter
  • Problem Solving with Areas
Circles, Arcs & Sectors
  • Area & Circumference of Circles
  • Arcs & Sectors
Volume & Surface Area
  • Volume
  • Surface Area
Congruence, Similarity & Geometrical Proof
  • Congruence
  • Similarity
  • Geometrical Proof
Area & Volume of Similar Shapes
  • Similar Area & Volumes
Right-Angled Triangles – Pythagoras & Trigonometry
  • Pythagoras Theorem
  • Right-Angled Trigonometry
  • Exact Trig Values
Sine, Cosine Rule & Area of Triangles
  • Sine & Cosine Rules
  • Area of a Triangle
  • Applications of Trigonomet
3D Pythagoras & Trigonometry
  • 3D Pythagoras & Trigonometry
Vectors
  • Introduction to Vectors
  • Working with Vectors
Transformations
  • Translations
  • Reflections
  • Rotations
  • Enlargements
  • Combination of Transformations
Probability Toolkit
  • Basic Probability
  • Relative & Expected Frequency
Simple Probability Diagrams
  • Two Way Tables
  • Frequency Trees
  • Set Notation & Venn Diagrams
Tree Diagrams
  • Tree Diagrams
Combined & Conditional Probability
  • Combined Probability
  • Conditional Probability
  • Combined Conditional Probabilities
Statistics Toolkit
  • Mean, Median & Mode
  • Averages from Tables
  • Range & Quartiles
  • Comparing Distributions
  • Population & Sampling
Statistical Diagrams
  • Bar Charts & Pictograms
  • Pie Charts
  • Time Series Graphs
  • Working with Statistical Diagrams
Histograms
  • Histograms
Cumulative Frequency & Box Plots
  • Cumulative Frequency Diagrams
  • Box Plots
Scatter Graphs & Correlation
  • Scatter Graphs