GCSE Maths

Numbers
32 Topics | 2 Quizzes
Integers
Integers Quiz
Prime Numbers and Composite Numbers
Positive and Negative Numbers
Order of Operations
Square Numbers and Cube Numbers
The Laws of Indices
Square Roots and Cube Roots
Triangular Numbers
The Fibonacci Sequence
Factors
Multiples
The Highest Common Factor
Fractions
Adding and Subtracting Fractions
Multiplication of Fractions
Division of Fractions
Fractional Indices
Decimal Places
Fractions and Decimals
Expressing Fractions as Decimal Numbers
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Algebra
29 Topics | 1 Quiz
Algebraic Notation
Algebraic Vocabulary
Collecting Like Terms
Substituting Values into Formulae
Rearranging Equations
Algebraic Fractions
Expanding Brackets and Simplifying
Expanding Double Brackets
Factorisation
Factorising Quadratic Expressions
Factorising Quadratics with a Coefficient of x Squared Greater than 1
The Quadratic Formula
The Difference of Two Squares
Subject of Formula
Solving Linear Equations
Quadratic Equations
Completing the Square
Sequences and Nth Term
Arithmetic and Geometric Sequences
Quadratic Sequences
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Ratio, Proportion and Rates of Change
7 Topics
Ratios
Scaling Ratios
Direct Proportion
Inverse Proportion
Reverse Percentages
Units and Conversions
Scale Factors
Geometry and Measures
16 Topics | 3 Quizzes
2D Shapes
2D Shapes Quiz
3D Shapes
3D Shapes Quiz
Types of angles
Angle Properties
Angle in Parallel Lines
Triangles
Triangles Quiz
Angles in Triangles
Polygons
Lines of Symmetry
Bearings
Loci and constructions
Constructing Triangles
Transformations
Enlargement
Plans and elevations
Areas and Volumes in Map Scale Problems
Probability
10 Topics
Introduction to Probability
Relative Frequency
Sample Space
Probability of Single Events
Probability of Combined Events
Probability Trees
Conditional probability
Set Notation
Venn diagrams
The Complement of a Set
Statistics
2 Topics
Population and samples
Representing data
Vectors
Mensuration and Calculation
7 Topics
Area
Volume
Congruence and similarity
Pythagoras’ theorem
Sine and cosine rule
Area of a triangle
Standard units of measure
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Standard Form

GCSE Maths Numbers Standard Form

Standard form is a convenient way to represent very small or very large numbers. A number written in standard form is expressed as A\times 10^{n}, where A\geq 1 but <10, and n is an integer.

In other words, 1\le A<10.

For example, the speed of light is approximately 299,793 , \text{km} , \text{s}^{-1}. In standard form, this is 2.99793\times 10^{5} , \text{km} , \text{s}^{-1} or, when rounded to three significant figures, 3\times 10^{5} , \text{km} , \text{s}^{-1}.

Let’s look at some more examples:

Examples of Standard Form

Example 1

Rewrite the following numbers in standard form:

a) 125,600,000,000

b) 1,300

c) 0.000001256

d) 0.0013

The standard form of these numbers is:

a) 1.256\times 10^{11}

b) 1.3\times 10^{3}

c) 1.256\times 10^{-6}

d) 1.3\times 10^{-3}

In these examples, A is a number such that 1\le A<10, and the power n is an integer. Large numbers greater than 10 have a positive n (e.g., a and b), while small numbers less than 1 have a negative n (e.g., c and d).

Example 2

Write down the following numbers in standard form:

i) 14,500,000

ii) 0.00000145

iii) 145

iv) 14.5

v) 0.145

In standard form, these numbers are:

i) 1.45\times 10^{7}

ii) 1.45\times 10^{-6}

iii) 1.45\times 10^{2}

iv) 1.45\times 10^{1}

v) 1.45\times 10^{-1}

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