1.3.1

Decimals

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Place Value

When a number is written out in digits each number stands for a different value depending on what position it takes in the number. For example in the number 7,342,176.525:

Hundreds

Hundreds

  • The number 1 stands for 100 since it is in the hundreds place.
Hundreds of thousands

Hundreds of thousands

  • The number 3 stands for 300,000 since it is in the hundreds of thousands place.

Adding Decimals

You should be able to add decimals without a calculator.

Step 1

Step 1

  • Move the decimal point two digits to the right (multiply by 100).
  • This gets rid of the decimals and lets us work with whole numbers.
Step 2

Step 2

  • Add the whole numbers together.
Step 3

Step 3

  • Re-introduce the decimals.
  • Move the decimal point two digits to the left (divide by 100).

Subtracting Decimals

You should be able to subtract decimals without a calculator.

Step 1

Step 1

  • Move the decimal point one digit to the right (multiply by 10).
  • This gets rid of the decimals and lets us work with whole numbers.
Step 2

Step 2

  • Calculate the difference between the whole numbers.
Step 3

Step 3

  • Re-introduce the decimals.
  • Move the decimal point one digit to the left (divide by 10).
Jump to other topics
1

Numbers

1.1

Integers

1.1.1Integers1.1.2Ordering Numbers1.1.3The Four Rules of Operations1.1.4Hierarchy of Operations1.1.5Definitions & Terms1.1.6HCF & LCM1.1.7Standard Form1.1.8Standard Form 21.1.9Prime Numbers1.1.10End of Topic Test - Standard Form
1.2

Fractions

1.2.1Fractions1.2.2Using Fractions1.2.3Conversion1.2.4Reciprocals
1.3

Decimals

1.3.1Decimals1.3.2Decimals 21.3.3Exam-Style Questions - Recurring Decimals1.3.4Comparing & Converting Decimals1.3.5End of Topic Test - Fractions & Decimals
1.4

Powers & Roots

1.4.1Square Numbers1.4.2Index Notation1.4.3Exam-Style Questions - Index Notation1.4.4Advanced Indices1.4.5Surds1.4.6End of Topic Test - Powers & Roots
1.5

Set Language & Notation

1.5.1Sets
1.6

Percentages

1.6.1Percentages1.6.2Percentage Change1.6.3Percentages in Finance1.6.4Compound Interest
1.7

Ratio & Proportion

1.7.1Manipulating Ratios1.7.2Proportion
1.8

Degree of Accuracy

1.8.1Rounding & Significant Figures1.8.2Estimation1.8.3Upper & Lower Bounds1.8.4Limits of Accuracy1.8.5Limits of Accuracy 21.8.6End of Topic Test - Rounding & Estimation
2

Equations, Formulae & Identities

2.1

Algebraic Manipulation

2.1.1Algebra Basics2.1.2Power Rules & Collecting Terms2.1.3Expanding Brackets2.1.4Expanding Brackets 22.1.5Factorising Quadratics2.1.6Algebraic Fractions2.1.7Proofs2.1.8End of Topic Test - Algebra & Proofs2.1.9Exam-Style Questions - Algebraic Proof
2.2

Expressions & Formulae

2.2.1Rearranging Formulae2.2.2Simple Formulae2.2.3End of Topic Test - Algebra Manipulation & Formula
2.3

Linear Equations

2.3.1Solving Linear Equations2.3.2Simultaneous Linear Equations
2.4

Quadratic Equations

2.4.1Solving Quadratics2.4.2Solving Quadratics 22.4.3End of Topic Test - Solving Equations2.4.4Simulateous Quadratic Equations2.4.5Exam-Style Questions - Simultaneous Equations2.4.6Graphs of Simultaneous Equations2.4.7End of Topic Test - Simultaneous Equations
2.5

Proportion

2.5.1Graphs & Proportion
2.6

Inequalities

2.6.1Solving Inequalities2.6.2Graphs of Inequalities2.6.3Exam-Style Questions - Inequalities2.6.4End of Topic Test - Inequalities
3

Sequences, Functions & Graphs

3.1

Sequences

3.1.1Sequence Rules3.1.2Finding Terms3.1.3Exam-Style Questions - Sequences3.1.4End of Topic Test - Sequences
3.2

Functions

3.2.1Functions3.2.2Composite & Inverse3.2.3End of Topic Test - Functions
3.3

Graphs

3.3.1Plotting Graphs3.3.2Straight Line Graphs3.3.3Properties of Graphs3.3.4Quadratic Graphs3.3.5Practical Graphs3.3.6Graphs of Polynomials3.3.7End of Topic Test Graphs
3.4

Common Graphs

3.4.1Graphs of Common Functions3.4.2Transformations of Graphs3.4.3End of Topic Test - Transformations and Graph
3.5

Calculus

3.5.1Derivatives of Functions3.5.2Maxima & Minima
4

Geometry

4.1

Angles, Lines & Triangles

4.1.1Angles & Lines4.1.2Angle Rules4.1.3Angles in Triangles4.1.4Exam-Style Questions - Angles
4.2

Polygons

4.2.1Polygons4.2.2Quadrilaterals4.2.3Congruence4.2.4Scale Factor4.2.5Exam-Style Questions - Enlargements4.2.6End of Topic Test - Geometry
4.3

Symmetry

4.3.1Symmetry4.3.2Exam-Style Questions - Reflection
4.4

Measures

4.4.1Measurements4.4.2Time4.4.3Bearings4.4.4Speed
4.5

Circle Properties

4.5.1Properties of a Circle4.5.2Circle Theorems4.5.3Circle Theorems 24.5.4Circle Theorems 34.5.5Exam-Style Questions - Circle Theorems
4.6

Trigonometry & Pythagoras’ theorem

4.6.1Pythagoras' Theorem4.6.2Trigonometry4.6.3Sine & Cosine for Obtuse Angles4.6.4Triangle Formulae4.6.5Exam-Style Questions - Trigonometry & Area
4.7

Mensuration of 2D Shapes

4.7.1Standard Units4.7.2Perimeter of 2D Shapes4.7.3Area of 2D Shapes4.7.4Area & Circumference of Circle4.7.5End of Topic Test - Trigonometry & Shapes
4.8

3D Shapes & Volume

4.8.13D Shapes4.8.2Surface Area4.8.3Volume4.8.4Exam-Style Questions - Volume
5

Vectors & Transformation Geometry

5.1

Vectors

5.1.1Vectors5.1.2Vectors 25.1.3Exam-Style Questions - Vectors
5.2

Transformation Geometry

5.2.1Transformations5.2.2Rotations5.2.3Translations & Reflections5.2.4Enlargements5.2.5Effects of Transformations
6

Statistics & Probability

6.1

Statistical Measures

6.1.1Basic Statistics6.1.2Frequency Table
6.2

Graphical Representation of Data

6.2.1Pictograms, Bar Charts & Pie Charts6.2.2Histograms6.2.3Cumulative Frequency6.2.4Cumulative Frequency 26.2.5Exam-Style Questions - Cumulative Frequency6.2.6End of Topic - Datasets
6.3

Probability

6.3.1Probability6.3.2Theoretical Probability6.3.3Experimental Probability6.3.4Venn Diagrams6.3.5Sample Space Diagrams6.3.6Tree Diagrams6.3.7Independent Events6.3.8Conditional Probability6.3.9End of Topic Test - Probability6.3.10Exam-Style Questions - Probability

Practice questions on Decimals

Can you answer these? Test yourself with free interactive practice on Seneca — used by over 10 million students.

  1. 1
    What does the 6 stand for in 8,375,693.1?Multiple choice
  2. 2
    What does the 5 stand for in 8,375,693.1?Multiple choice
  3. 3
    What does the 1 stand for in 8,375,693.1?Multiple choice
  4. 4
    What does the 7 stand for in 7,414,311.8?Multiple choice
  5. 5
    What does the 3 stand for in 7,414,311.8?Multiple choice
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Reciprocals

Decimals 2