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DP IB Maths: AA SL

Revision Notes

Home / IB / Maths: AA SL / DP / Revision Notes / 1. Number & Algebra / 1.1 Number Toolkit / 1.1.1 Standard Form


1.1.1 Standard Form


Standard Form

Standard form (sometimes called scientific notation or standard index form) gives us a way of writing very big and very small numbers using powers of 10.

Why use standard form?

  • Some numbers are too big or too small to write easily or for your calculator to display at all
    • Imagine the number 5050 , the answer would take 84 digits to write out
    • Try typing 5050 into your calculator, you will see it displayed in standard form
  • Writing very big or very small numbers in standard form allows us to:
    • Write them more neatly
    • Compare them more easily
    • Carry out calculations more easily
  • Exam questions could ask for your answer to be written in standard form

 

How is standard form written?

  • In standard form numbers are always written in the form a cross times 10 to the power of k where a and k satisfy the following conditions:
    • 1 space less or equal than a less than 10
      • So there is one non – zero digit before the decimal point
    • k space element of straight integer numbers 
      • So k must be an integer
    • k greater than 0 for large numbers
      • How many times a is multiplied by 10
    • k less than 0 for small numbers
      • How many times a is divided by 10

 

How are calculations carried out with standard form? 

  • Your GDC will display large and small numbers in standard form when it is in normal mode
    • Your GDC may display standard form as aEn
      • For example, 2.1 space cross times space 10 to the power of negative 5 end exponent will be displayed as 2.1 straight E minus 5
      • If so, be careful to rewrite the answer given in the correct form, you will not get marks for copying directly from your GDC
  • Your GDC will be able to carry out calculations in standard form
    • If you put your GDC into scientific mode it will automatically convert numbers into standard form
      • Beware that your GDC may have more than one mode when in scientific mode
      • This relates to the number of significant figures the answer will be displayed in
      • Your GDC may add extra zeros to fill spaces if working with a high number of significant figures, you do not need to write these in your answer
  • To add or subtract numbers written in the form a space cross times space 10 to the power of k without your GDC you will need to write them in full form first
  • To multiply or divide numbers written in the form a space cross times space 10 to the power of k without your GDC you can either write them in full form first or use the laws of indices

Exam Tip

  • Your GDC will give very big or very small answers in standard form and will have a setting which will allow you to carry out calculations in scientific notation
  • Make sure you are familiar with the form that your GDC gives answers in as it may be different to the form you are required to use in the exam

Worked Example

Calculate the following, giving your answer in the form a cross times 10 to the power of k, where 1 less or equal than a less than 10 space and k element of straight integer numbers.

 

i)
3780 space cross times space 200ai-sl-1-1-1-we-1-standard-form-part-i

 

 ii)   left parenthesis 7 space cross times space 10 to the power of 5 right parenthesis space minus space left parenthesis 5 space cross times space 10 to the power of 4 right parenthesis

ai-sl-1-1-1-we-1-standard-form-part-ii

 

iii)
left parenthesis 3.6 cross times 10 to the power of negative 3 end exponent right parenthesis left parenthesis 1.1 cross times 10 to the power of negative 5 end exponent right parenthesisai-sl-1-1-1-we-1-standard-form-part-iii



  • 1. Number & Algebra
    • 1.1 Number Toolkit
      • 1.1.1 Standard Form
        • 1.1.2 Laws of Indices
        • 1.2 Exponentials & Logs
          • 1.2.1 Introduction to Logarithms
            • 1.2.2 Laws of Logarithms
              • 1.2.3 Solving Exponential Equations
              • 1.3 Sequences & Series
                • 1.3.1 Language of Sequences & Series
                  • 1.3.2 Arithmetic Sequences & Series
                    • 1.3.3 Geometric Sequences & Series
                      • 1.3.4 Applications of Sequences & Series
                        • 1.3.5 Compound Interest & Depreciation
                        • 1.4 Proof & Reasoning
                          • 1.4.1 Proof
                          • 1.5 Binomial Theorem
                            • 1.5.1 Binomial Theorem
                          • 2. Functions
                            • 2.1 Linear Functions & Graphs
                              • 2.1.1 Equations of a Straight Line
                              • 2.2 Quadratic Functions & Graphs
                                • 2.2.1 Quadratic Functions
                                  • 2.2.2 Factorising & Completing the Square
                                    • 2.2.3 Solving Quadratics
                                      • 2.2.4 Quadratic Inequalities
                                        • 2.2.5 Discriminants
                                        • 2.3 Functions Toolkit
                                          • 2.3.1 Language of Functions
                                            • 2.3.2 Composite & Inverse Functions
                                              • 2.3.3 Graphing Functions
                                              • 2.4 Further Functions & Graphs
                                                • 2.4.1 Reciprocal & Rational Functions
                                                  • 2.4.2 Exponential & Logarithmic Functions
                                                    • 2.4.3 Solving Equations
                                                      • 2.4.4 Modelling with Functions
                                                      • 2.5 Transformations of Graphs
                                                        • 2.5.1 Translations of Graphs
                                                          • 2.5.2 Reflections of Graphs
                                                            • 2.5.3 Stretches of Graphs
                                                              • 2.5.4 Composite Transformations of Graphs
                                                            • 3. Geometry & Trigonometry
                                                              • 3.1 Geometry Toolkit
                                                                • 3.1.1 Coordinate Geometry
                                                                  • 3.1.2 Radian Measure
                                                                    • 3.1.3 Arcs & Sectors
                                                                    • 3.2 Geometry of 3D Shapes
                                                                      • 3.2.1 3D Coordinate Geometry
                                                                        • 3.2.2 Volume & Surface Area
                                                                        • 3.3 Trigonometry
                                                                          • 3.3.1 Pythagoras & Right-Angled Triganometry
                                                                            • 3.3.2 Non Right-Angled Trigonometry
                                                                              • 3.3.3 Applications of Trigonometry & Pythagoras
                                                                              • 3.4 Further Trigonometry
                                                                                • 3.4.1 The Unit Circle
                                                                                  • 3.4.2 Exact Values
                                                                                  • 3.5 Trigonometric Functions & Graphs
                                                                                    • 3.5.1 Graphs of Trigonometric Functions
                                                                                      • 3.5.2 Transformations of Trigonometric Functions
                                                                                        • 3.5.3 Modelling with Trigonometric Functions
                                                                                        • 3.6 Trigonometric Equations & Identities
                                                                                          • 3.6.1 Simple Identities
                                                                                            • 3.6.2 Double Angle Formulae
                                                                                              • 3.6.3 Relationship Between Trigonometric Ratios
                                                                                                • 3.6.4 Linear Trigonometric Equations
                                                                                                  • 3.6.5 Quadratic Trigonometric Equations
                                                                                                • 4. Statistics & Probability
                                                                                                  • 4.1 Statistics Toolkit
                                                                                                    • 4.1.1 Sampling & Data Collection
                                                                                                      • 4.1.2 Statistical Measures
                                                                                                        • 4.1.3 Frequency Tables
                                                                                                          • 4.1.4 Linear Tranformations of Data
                                                                                                            • 4.1.5 Outliers
                                                                                                              • 4.1.6 Univariate Data
                                                                                                                • 4.1.7 Interpreting Data
                                                                                                                • 4.2 Correlation & Regression
                                                                                                                  • 4.2.1 Bivariate Data
                                                                                                                    • 4.2.2 Correlation & Regression
                                                                                                                    • 4.3 Probability
                                                                                                                      • 4.3.1 Probability & Types of Events
                                                                                                                        • 4.3.2 Conditional Probability
                                                                                                                          • 4.3.3 Sample Space Diagrams
                                                                                                                          • 4.4 Probability Distributions
                                                                                                                            • 4.4.1 Discrete Probability Distributions
                                                                                                                              • 4.4.2 Expected Values
                                                                                                                              • 4.5 Binomial Distribution
                                                                                                                                • 4.5.1 The Binomial Distribution
                                                                                                                                  • 4.5.2 Calculating Binomial Probabilities
                                                                                                                                  • 4.6 Normal Distribution
                                                                                                                                    • 4.6.1 The Normal Distribution
                                                                                                                                      • 4.6.2 Calculations with Normal Distribution
                                                                                                                                        • 4.6.3 Standardisation of Normal Variables
                                                                                                                                      • 5. Calculus
                                                                                                                                        • 5.1 Differentiation
                                                                                                                                          • 5.1.1 Introduction to Differentiation
                                                                                                                                            • 5.1.2 Applications of Differentiation
                                                                                                                                            • 5.2 Further Differentiation
                                                                                                                                              • 5.2.1 Differentiating Special Functions
                                                                                                                                                • 5.2.2 Techniques of Differentiation
                                                                                                                                                  • 5.2.3 Second Order Derivatives
                                                                                                                                                    • 5.2.4 Further Applications of Differentiation
                                                                                                                                                      • 5.2.5 Concavity & Points of Inflection
                                                                                                                                                        • 5.2.6 Derivatives & Graphs
                                                                                                                                                        • 5.3 Integration
                                                                                                                                                          • 5.3.1 Introduction to Integration
                                                                                                                                                            • 5.3.2 Applications of Integration
                                                                                                                                                            • 5.4 Further Integration
                                                                                                                                                              • 5.4.1 Integrating Special Functions
                                                                                                                                                                • 5.4.2 Techniques of Integration
                                                                                                                                                                  • 5.4.3 Definite Integrals
                                                                                                                                                                    • 5.4.4 Further Applications of Integration
                                                                                                                                                                    • 5.5 Optimisation
                                                                                                                                                                      • 5.5.1 Modelling with Differentiation
                                                                                                                                                                      • 5.6 Kinematics
                                                                                                                                                                        • 5.6.1 Kinematics Toolkit
                                                                                                                                                                          • 5.6.2 Calculus for Kinematics
                                                                                                                                                                        Amber Perry

                                                                                                                                                                        Author: Amber

                                                                                                                                                                        Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.


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