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Standard form

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Qualitative and quantitative data

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Relative frequency

Listing outcomes

Venn diagrams

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Pythagoras’ theorem

Trigonometric ratios: SOH CAH TOA

Finding missing lengths in a triangle

Finding missing angles in a triangle

Drawing shapes

Transformations

Constructions

Constructing triangles

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Types of angles

Angle rules

Interior and exterior angles

Parallel lines

Measures

Area and perimeter: Triangles and quadrilaterals

Area of compound shapes

Volume of prisms

Properties of shapes

Symmetrical shapes and rotational symmetry

Congruent shapes

Similar shapes

Nets and surface area

Shapes

Quadrilaterals: Types and properties

Triangles and regular polygons: Types and properties

Circles: Area and circumference

3D shapes: Identification and properties

Rates of change

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Conversion factors

Imperial units

Solving best buy problems

Reading timetables

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Speed: Formula and units

Density: Formula and units

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Interpreting graphs

Solving simultaneous equations using graphs

Quadratic graphs

Travel graphs: Distance-time graphs

Conversion graphs

Straight line graphs

X and Y coordinates

Straight line graphs

Drawing straight line graphs

Finding the gradient

Equation of a straight line: y = mx + c

Drawing a graph of a linear equation

Estimating values using linear graphs

Formulae and equations

Substituting numbers into an expression

Writing and using formulae

Solving equations

Rearranging formulae

Number patterns and sequences

The nth term

Inequalities: Greater than or less than

Simultaneous equations

Algebraic manipulation

Algebraic notation

Algebraic terms

Simplifying algebraic expressions

Multiplying and dividing algebraic expressions

Single brackets: Expanding and factorising

Expanding double brackets: FOIL and multiplication grid

Fractions, decimals and percentages

Converting between fractions, decimals and percentages

Fractions

Fraction operations: Add, subtract, multiply, divide

Percentages

Rounding: Decimal places and significant figures

Rounding errors and estimating

Number calculations

Ordering numbers: Whole numbers and decimals

Addition and subtraction using the column method

Multiplying and dividing by powers of 10

Adding and subtracting decimals

Methods for multiplication and division

Order of operations: BIDMAS

Types of numbers

Understanding place value

Negative numbers: Add, subtract, multiply, divide

Special types of numbers

Multiples, factors and prime factors

Lowest common multiple and highest common factor

Square roots and cube roots

Writing indices and index laws

Standard form

Explainer Video

Tutor: Bilal

Summary

Standard form

In a nutshell

Standard index form (or standard form) is a convenient way of writing very large or very small numbers.

What does standard form look like?

A number is in standard index form if it is written in the form:

$a\times10^b$

Where the number $a$ is always between $1$ and $10$ , and $b$ is a whole number.

Writing a number in standard form

To write a number in standard index form, follow this procedure.

procedure

1.	Move the decimal point until the number is between $1$ and $10$ . Count how many spaces the decimal point was moved.
2.	This number between $1$ and $10$ is the value of $a$ .
3.	The number of spaces the decimal point was moved is the value of $b$ . If the decimal point moved to the left, then $b$ is positive. If the decimal point was moved to the right, then $b$ is negative.

Example 1

What is $76000$ in standard index form?

First, write $76000$ as $76000.00$ and move the decimal point until the number is between $1$  and $10$ :

$7\overset{\curvearrowleft \curvearrowleft \curvearrowleft \curvearrowleft}{.6\, 0\,0\,0\,}0\thinspace 0$ , so $a=7.6$ 

The decimal point moved $4$ spaces to the left, so $b=4$ .

$\underline{76000=7.6\times10^4}$

Example 2

What is $0.0000815$ in standard index form?

First, move the decimal point until the number is between $1$ and $10$ :

$0\thinspace \overset{\curvearrowright \curvearrowright \curvearrowright \curvearrowright \curvearrowright}{0\,0\,0\,0\,8.}15$ , so $a=8.15$

The decimal point moved $5$ spaces to the right, so $b=-5$ .

$\underline{0.0000815=8.15\times10^{-5}}$ 

Multiplying and dividing in standard form

To multiply and divide two numbers in standard form, use your calculator to multiply the numbers. Then, make any adjustments if necessary to make sure the answer is in standard form.

Example 3

What is $(1.5\times10^8)\times(9\times10^{-3})$ ?

Using the calculator gives:

$(1.5\times10^8)\times(9\times10^{-3})=1350000$

Convert $1350000$ into standard form:

$1350000=1.35\times10^6$

$\underline{(1.5\times10^8)\times(9\times10^{-3})=1.35\times10^6}$

Learn with Basics

Length:

Unit 1

Writing indices and index laws

Jump Ahead

Optional

Unit 2

Standard form

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

How do you multiply and divide two numbers in standard form?

Multiply/divide with your calculator. Then, convert it back to standard index form using the usual method.

How do you write a number in standard form?

Move the decimal point until the number is between 1 and 10. This is the value of a. The number of spaces the decimal point moved is the value of b. If the decimal point moved to the left the value of b will be positive.

What is standard index form?

Standard index form is when a number is written in the form a x 10^b, where a is between 1 and 10 and b is an integer.

Home

Maths

Types of numbers

Standard form

Videos

Summary

Exercises

Select Lesson

Statistics

Qualitative and quantitative data

Representing data: Graphs and charts

Mean, median, mode and range

Frequency tables

Averages from frequency tables

Averages from grouped frequency tables

Scatter graphs

Probability

Calculating probability

Equal and unequal probabilities

Relative frequency

Listing outcomes

Venn diagrams

Trigonometry

Pythagoras’ theorem

Trigonometric ratios: SOH CAH TOA

Finding missing lengths in a triangle

Finding missing angles in a triangle

Drawing shapes

Transformations

Constructions

Constructing triangles

Lines and angles

Types of angles

Angle rules

Interior and exterior angles

Parallel lines

Measures

Area and perimeter: Triangles and quadrilaterals

Area of compound shapes

Volume of prisms

Properties of shapes

Symmetrical shapes and rotational symmetry

Congruent shapes

Similar shapes

Nets and surface area

Shapes

Quadrilaterals: Types and properties

Triangles and regular polygons: Types and properties

Circles: Area and circumference

3D shapes: Identification and properties

Rates of change

Percentage change

Conversion factors

Imperial units

Solving best buy problems

Reading timetables

Maps and scale drawings

Speed: Formula and units

Density: Formula and units

Proportion

Ratio

Other graphs

Interpreting graphs

Solving simultaneous equations using graphs

Quadratic graphs

Travel graphs: Distance-time graphs

Conversion graphs

Straight line graphs

X and Y coordinates

Straight line graphs

Drawing straight line graphs

Finding the gradient

Equation of a straight line: y = mx + c

Drawing a graph of a linear equation

Estimating values using linear graphs

Formulae and equations

Substituting numbers into an expression

Writing and using formulae

Solving equations

Rearranging formulae

Number patterns and sequences

The nth term

Inequalities: Greater than or less than

Simultaneous equations

Algebraic manipulation

Algebraic notation

Algebraic terms

Simplifying algebraic expressions

Multiplying and dividing algebraic expressions

Single brackets: Expanding and factorising

Expanding double brackets: FOIL and multiplication grid

Fractions, decimals and percentages

Converting between fractions, decimals and percentages

Fractions

Fraction operations: Add, subtract, multiply, divide

Percentages

Rounding: Decimal places and significant figures

Rounding errors and estimating

Number calculations

Ordering numbers: Whole numbers and decimals

Addition and subtraction using the column method

Multiplying and dividing by powers of 10

Adding and subtracting decimals

Methods for multiplication and division

Order of operations: BIDMAS

Types of numbers

Understanding place value

Negative numbers: Add, subtract, multiply, divide

Special types of numbers

Multiples, factors and prime factors

Lowest common multiple and highest common factor

Square roots and cube roots

Writing indices and index laws

Standard form

Explainer Video

Tutor: Bilal

Summary

Standard form

In a nutshell

Standard index form (or standard form) is a convenient way of writing very large or very small numbers.

What does standard form look like?

A number is in standard index form if it is written in the form:

$a\times10^b$

Where the number $a$ is always between $1$ and $10$ , and $b$ is a whole number.

Writing a number in standard form

To write a number in standard index form, follow this procedure.

procedure

1.	Move the decimal point until the number is between $1$ and $10$ . Count how many spaces the decimal point was moved.
2.	This number between $1$ and $10$ is the value of $a$ .
3.	The number of spaces the decimal point was moved is the value of $b$ . If the decimal point moved to the left, then $b$ is positive. If the decimal point was moved to the right, then $b$ is negative.

Example 1

What is $76000$ in standard index form?

First, write $76000$ as $76000.00$ and move the decimal point until the number is between $1$  and $10$ :

$7\overset{\curvearrowleft \curvearrowleft \curvearrowleft \curvearrowleft}{.6\, 0\,0\,0\,}0\thinspace 0$ , so $a=7.6$ 

The decimal point moved $4$ spaces to the left, so $b=4$ .

$\underline{76000=7.6\times10^4}$

Example 2

What is $0.0000815$ in standard index form?

First, move the decimal point until the number is between $1$ and $10$ :

$0\thinspace \overset{\curvearrowright \curvearrowright \curvearrowright \curvearrowright \curvearrowright}{0\,0\,0\,0\,8.}15$ , so $a=8.15$

The decimal point moved $5$ spaces to the right, so $b=-5$ .

$\underline{0.0000815=8.15\times10^{-5}}$ 

Multiplying and dividing in standard form

To multiply and divide two numbers in standard form, use your calculator to multiply the numbers. Then, make any adjustments if necessary to make sure the answer is in standard form.

Example 3

What is $(1.5\times10^8)\times(9\times10^{-3})$ ?

Using the calculator gives:

$(1.5\times10^8)\times(9\times10^{-3})=1350000$

Convert $1350000$ into standard form:

$1350000=1.35\times10^6$

$\underline{(1.5\times10^8)\times(9\times10^{-3})=1.35\times10^6}$

Learn with Basics

Length:

Unit 1

Writing indices and index laws

Jump Ahead

Optional

Unit 2

Standard form

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

How do you multiply and divide two numbers in standard form?

Multiply/divide with your calculator. Then, convert it back to standard index form using the usual method.

How do you write a number in standard form?

What is standard index form?

Standard index form is when a number is written in the form a x 10^b, where a is between 1 and 10 and b is an integer.

Standard form

Videos

Summary

Exercises

Select Lesson

Statistics

Probability

Trigonometry

Drawing shapes

Lines and angles

Measures

Properties of shapes

Shapes

Rates of change

Proportion

Ratio

Other graphs

Straight line graphs

Formulae and equations

Algebraic manipulation

Fractions, decimals and percentages

Number calculations

Types of numbers

Explainer Video

Summary

Standard form

​​In a nutshell

What does standard form look like?

Writing a number in standard form

procedure

Example 1

Example 2

Multiplying and dividing in standard form

Example 3

Learn with Basics

Unit 1

Writing indices and index laws

Jump Ahead

Unit 2

Standard form

Final Test

FAQs - Frequently Asked Questions

How do you multiply and divide two numbers in standard form?

How do you write a number in standard form?

What is standard index form?

Standard form

Videos

Summary

Exercises

Select Lesson

Statistics

Probability

Trigonometry

Drawing shapes

Lines and angles

Measures

Properties of shapes

Shapes

Rates of change

Proportion

Ratio

Other graphs

Straight line graphs

Formulae and equations

Algebraic manipulation

Fractions, decimals and percentages

Number calculations

Types of numbers

Explainer Video

Summary

Standard form

​​In a nutshell

What does standard form look like?

Writing a number in standard form

procedure

Example 1

Example 2

Multiplying and dividing in standard form

Example 3

Learn with Basics

In a nutshell

In a nutshell