GCSE Maths

Numbers
37 Topics | 1 Quiz
Expressing Fractions as Decimal Numbers
Nearest 10, 100, 1000, …
Nearest 10, 100, 1000, 10000, …, million and so on
Percentages
More on Percentages: Applications to Interest Calculations
Significant Figures
Significant Figures
Rounding Up and Estimation
Standard Form
Order of Operations
Four Operational Rules
Square Roots and Cube Roots
Conversion of Units to other Units
Compound Interest
Surds
Rational and Irrational Numbers
Errors and Uncertainties in Measurements
Greatest and Least Possible Values
2 of 2
Vectors
1 Topic
Vectors
Probability
6 Topics
Introduction to probability
Finding the sum of probabilities
Conditional probability
Set Notation
Venn diagrams
The Complement of a Set
Statistics
2 Topics
Population and samples
Representing data
Algebra
16 Topics | 1 Quiz
Algebraic Notation
Algebraic Vocabulary
Collecting Like Terms
Expanding Brackets and Simplifying
Expanding Double Brackets
The Difference of Two Squares
Substituting into Formulae
Subject of Formula
Factorisation
Factorising Quadratic Expressions
More on Factorisation
Equations
Quadratic Equations
Mathematical Formulae
Algebraic Equivalence and Proof
Functions
Algebra
Sequences
2 Topics | 1 Quiz
Generating sequences
Nth Term Sequences
Sequences
Ratio, Proportion and Rates of Change
8 Topics | 1 Quiz
Inverse Proportion
Conversion
Scale Factors
Percentages
Direct Proportion
Rate, Ratio and Proportion Examples
Ratios
Ratios
Ratio, Proportion and Rates of Change
Geometry and Measures
9 Topics
Loci and constructions
Properties of angles
Properties of polygons
Transformations
Enlargement
Circle theorems
Plane figure properties
Plans and elevations
Areas and Volumes in Map Scale Problems
Mensuration and Calculation
10 Topics
Map scales
Bearings
Area
Volume
Circles: arcs and sectors
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

We usually write very small numbers or very large numbers in standard form. To write a number in standard form, we write it as A\times 10^{ n }, where A\geq 1 but <10.

So, 1\le A<10

and n is an integer.

For example, the speed of light is 299,793kms^{-1}. In standard form, this is 2.99793\times 10^{5} kms^{-1} or 3\times 10^{5} kms^{-1} in standard form, correct to three significant figures.

Let’s look at some more examples:

Example

Rewrite in standard form:
a) 125600000000

*** QuickLaTeX cannot compile formula:
</span><strong><span class="has-inline-color has-vivid-green-cyan-color">b) </span></strong><span class="has-inline-color has-black-color">1300 </span><span class="has-inline-color has-vivid-green-cyan-color">c)</span><span class="has-inline-color has-black-color"> 0.000001256 </span><strong><span class="has-inline-color has-vivid-green-cyan-color">d)</span></strong><span class="has-inline-color has-black-color"> 0.00013</span>
<!-- /wp:paragraph -->

<!-- wp:paragraph -->
<strong><span class="has-inline-color has-vivid-green-cyan-color">a)</span></strong><span class="has-inline-color has-black-color">

*** Error message:
Missing $ inserted.
125,600,000,000=1.256\times 10^{ 11 }</span><strong><span class="has-inline-color has-vivid-green-cyan-color">b)</span></strong><span class="has-inline-color has-black-color">13,000=1.3\times 10^{ 4 }</span><strong><span class="has-inline-color has-vivid-green-cyan-color">c)</span></strong><span class="has-inline-color has-black-color">0.000001256=1.256\times 10^{ -6 }</span><strong><span class="has-inline-color has-vivid-green-cyan-color">d)</span></strong><span class="has-inline-color has-black-color">0.0013=1.3\times 10^{ -4 }
*** QuickLaTeX cannot compile formula:
</span>
<!-- /wp:paragraph -->

<!-- wp:paragraph -->
<span class="has-inline-color has-black-color">In the above,

*** Error message:
Missing $ inserted.
Ais a number such that1\le A<10and the indexnis an integer.Large numbers greater than10will havenpositive as in a) and b) and small numbers less than1will haven
*** QuickLaTeX cannot compile formula:
negative as in c) and d).</span>
<!-- /wp:paragraph -->

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<h2 id="h-example-1"><span class="has-inline-color has-luminous-vivid-orange-color">Example</span></h2>
<!-- /wp:heading -->

<!-- wp:paragraph -->
Write down the following numbers in standard form:
<!-- /wp:paragraph -->

<!-- wp:paragraph -->
<strong><span class="has-inline-color has-vivid-green-cyan-color">i)</span></strong> 14500000
<!-- /wp:paragraph -->

<!-- wp:paragraph -->
<strong><span class="has-inline-color has-vivid-green-cyan-color">ii)</span></strong> 0.00000145
<!-- /wp:paragraph -->

<!-- wp:paragraph -->
<strong><span class="has-inline-color has-vivid-green-cyan-color">iii)</span></strong> 145
<!-- /wp:paragraph -->

<!-- wp:paragraph -->
<strong><span class="has-inline-color has-vivid-green-cyan-color">iv) </span></strong>14.5
<!-- /wp:paragraph -->

<!-- wp:paragraph -->
<strong><span class="has-inline-color has-vivid-green-cyan-color">v)</span></strong> 0.145
<!-- /wp:paragraph -->

<!-- wp:paragraph -->
In standard form, these are:
<!-- /wp:paragraph -->

<!-- wp:paragraph -->
<strong><span class="has-inline-color has-vivid-green-cyan-color">i)</span></strong>

*** Error message:
Missing $ inserted.
1.45\times 10^{7}
*** QuickLaTeX cannot compile formula:

<!-- /wp:paragraph -->

<!-- wp:paragraph -->
<strong><span class="has-inline-color has-vivid-green-cyan-color">ii)</span></strong><span class="has-inline-color has-black-color">

*** Error message:
Missing $ inserted.
1.45\times 10^{-6}
*** QuickLaTeX cannot compile formula:
</span>
<!-- /wp:paragraph -->

<!-- wp:paragraph -->
<strong><span class="has-inline-color has-vivid-green-cyan-color">iii)</span></strong><span class="has-inline-color has-black-color">

*** Error message:
Missing $ inserted.
1.45\times 10^{2}
*** QuickLaTeX cannot compile formula:
</span>
<!-- /wp:paragraph -->

<!-- wp:paragraph -->
<strong><span class="has-inline-color has-vivid-green-cyan-color">iv)</span></strong><span class="has-inline-color has-black-color">

*** Error message:
Missing $ inserted.
1.45\times 10
*** QuickLaTeX cannot compile formula:
</span>
<!-- /wp:paragraph -->

<!-- wp:paragraph -->
<strong><span class="has-inline-color has-vivid-green-cyan-color">v)</span></strong><span class="has-inline-color has-black-color">

*** Error message:
Missing $ inserted.
1.45\times 10^{-1}$

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