In this lesson we will learn how to convert numbers into scientific notations. Scientific notation is a form of writing or expressing a very large or a very small number. It is composed of a whole number and its exponent.

**Example:**

- 2 x 10
^{8} - 5 x 10
^{-6} - 6 x 10
^{4} - 4 x 10
^{-8}

Sometimes, because numbers are so large, mathematicians use scientific notations to express it simply. This is done to save space and make it convenient for both the reader and author.

It is easy to convert large numbers into scientific notation. Just follow these steps:

- Always put in mind that any whole number can also be written in a decimal form

3800000 = 3800000.0 - Then move the decimal point to the left until you have a number that is between 1 and 10.

Based from the example number above, moving the decimal point to the left will give 3.8 - Now, let us count the number of times we have moved the decimal point

Based again on the above example, you have moved the decimal point 6 places to the left - We can now express that we have moved the decimal point 6 places to the left by writing 10
^{6}

The scientific notation therefore of 3800000 is 3.8 x 10^{6}

3.8 x 10^{6}= 3.8 x 10 x 10 x 10 x 10 x 10 x 10

3.8 x 10^{6}= 3800000

- 45600000000

45600000000 = 45600000000.0

45600000000 = 4.56 x 10^{10} - 37000

37000 = 37000.0

37000 = 3.7 x 10^{4} - 5600000000

5600000000 = 5600000000.0

5600000000 = 5.6 x 10^{9} - 67980000000

67980000000 = 67980000000.0

67980000000 = 6.798 x 10^{10} - 50700000

50700000 = 50700000.0

50700000 = 5.07 x 10^{7}

Mathematicians and scientists also use scientific notations for very small numbers. This is done to make writing

them easy and convenient.

Converting very small numbers into scientific notation is also simple. Just follow these rules:

0.00000078

- Move the decimal point to the right until you have a number that is between 1 and 10.

Based from the example number above, moving the decimal point to the left would make it to 7.8 - Now, let us count the number of times we have moved the decimal point

Based again on the above example, you have moved the decimal point 7 places to the right - We can now express that we have moved the decimal point 7 places to the right by writing 10
^{-7}

The scientific notation therefore of 0.00000078 is 7.8 x 10^{-7}

7.8 x 10^{-7} = 3.8 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1

7.8 x 10^{-7} = 0.00000078

AtHome Tuition provides students with all the tools needed for problem solving, reasoning, communicating and

connecting with regard to succeeding in math. We follow a curriculum that is based on the unique needs of each

individual student, so that they can learn math online to the highest of standards. Our math programs help students

to make connections and build relationships between its different aspects, including algebra, arithmetic, geometry,

discrete math, probability and statistics.

Students are encouraged to talk about mathematics when they learn math online. They are taught to use the

specific language and symbols of mathematics to communicate and discuss problems and their solutions.

Students will be able to develop both their competence and their confidence in mathematics when they learn math

online with AtHome Tuition.

** We offer the following Mathematics programs: **

**Basic Mathematics**

Our basic program enables students to learn math online and master basic knowledge of algebra, patterns

and functions.

** The personalized curriculum includes: **

- Expressions
- Equations
- Inequalities
- Numeric and Graphic Representations
- Problem Solving
- Measurement
- Patterns and Functions

Our pre-Algebra program allows students to learn math online by reviewing and understanding all of the basic concepts of Algebra. Our highly-skilled teachers help the students to understand the concept of Pre-Algebra in a systematic, yet simple manner. Once the student's current knowledge level has been assessed, the teacher will work on the gaps in their skills and help to build the students self-confidence. New concepts are taught in incremental stages, and our tutoring will be synchronized with the student's school lessons in order to get them to the top of the class. Our teachers can also provide students who learn math online help with school homework and test preparation

** Included in the curriculum are: **

- Problem Solving
- Patterns and Functions
- Measurement

This program helps students with analysis of the patterns and functional relationships by using mathematical

language and the appropriate technology.

** The curriculum includes: **

- Equations and Inequalities
- Functions and their representations
- Algebraic Expressions
- Statistics and Probability
- Critical Thinking and Reasoning

Learn math online with the Algebra II program. We will educate students on how to algebraically represent,

model, analyze and solve mathematical and real world problems that involve functional patterns and relationships.

** Included in the curriculum are the following units **

- Equations and Inequalities
- Exponential Patterns
- Functions and Relations
- Rational Numbers
- Probabilities
- Statistics

The trigonometry program can enable students that learn math online to understand all the trigonometric functions and their use in solving trigonometric equations that include both infinitive solutions and restricted domain The teaching method includes the use of graphing utilities that can solve equations, check for reasonableness of solutions. results, and verify algebraic solutions.

** Our trigonometry curriculum includes: **

- Trigonometric Functions
- Inverse Trigonometric Functions
- Graphing of Trigonometric Functions
- Complex Numbers and Polar Coordinates
- Exponential and logarithmic functions

Our Pre-Calculus program is of immeasurable benefit for students who learn math online. The program enables students to represent functions and relations numerically, graphically, and algebraically. Students will use numerical, algebraic, and graphical representations of functions and relations in order to solve real-world problems.

** The curriculum covers: **

- Rational Functions
- Functions and Graphing

The program will provide students with a solid foundation of mathematical concepts that include limits, infinity, and changes in quantities over time. Students learn math online by collecting data, generating graphs and analyzing the results of real world situations that can be described by linear, quadratic, trigonometric, and exponential models.

** Models covered in the curriculum: **

- Limits
- Derivatives
- Integral

- Absolute Values
- Adding and Subtracting Fractions
- Addition of Decimals
- Algebra Linear Equations
- Algebra Quadratic Equations
- Algebra Simultaneous Equations
- Algebraic Properties
- Algebraic Function
- Analyzing and Integrating
- Asymptotes
- Bar Graphs
- Basics of Statistics
- Circular Permutations
- Combinations
- Complex Numbers
- Complex Numbers AddSub
- Complex Numbers Division
- ComplexNumbers Multiplication
- Complex Numbers Properties
- Composite Functions
- Cube and Cube Roots
- Data collection Add Multipli Rules
- Datacollection GroupedMean
- Datacollection Mean
- Datacollection Median
- Datacollection Mode
- Datacollection Probabilitybasics
- Datacollection Probabilityevents
- Dividing Rational Numbers
- Division of Decimals
- Domain of SquareRootFunction
- EquationsReducibleQuadratic
- Exponential Functions
- ExponentialLogarithmicFunction
- Factorization
- FactorizationAnyQPolynomial
- FactorizationMonicQPolynomial
- Fractions & Decimal Conversion
- Functions
- Geometry Basics
- Graph of Rational Functions
- Graph of SquareRootFunction
- GraphicalRepresentation
- Graph of Complex Numbers
- Graphs Functions
- HighestCommonFactor
- Inequalities
- Inverse Square Functions
- Inverse of a Function
- Justifying Solutions
- LeastCommonMultiple
- Linear Equations2Variables
- LinearEquations3Variables
- Linear Equation System
- Linear Equation Graphs
- Linear Inequalities Graphs
- Maxima Minima Zeros
- More Functions
- Multiplication of Decimals
- Multiplying Rational Numbers
- Multiplying Two Polynomials
- Other Functions
- Permutations
- Pictorial BarChart
- Pictorial Bivariatedata
- Pictorial BoxPlots
- Pictorial FrequencyTable
- Pictorial Histogram
- Pictorial LineCharts
- Pictorial PieChart
- Pictorial StemLeafPlot
- Polynomials Addition
- Polynomials Division
- Polynomials Multiplication
- Predicting Values
- Problem Solving Strategies
- Quadratic Equation
- QuadraticEquationsFormula
- QuadraticEquationsSolutions
- QuadraticInequalities
- Rational Behind Functions
- Rational Expression
- Rational Functions
- Real Numbers
- Reciprocal Functions
- Recursive Multiplication
- Rational Numbers
- Review of functions
- Review of Sets and Relations
- Rounding Numbers
- Scientific Notation
- Simple Probabilities
- SimplifyingRationalExpressions
- SolutionQuadratEquawhen
- Solving Fractions
- SolvingQuadraticEquations
- Square of a Binomial
- SquareRootFunctions
- SquareRootFunInequalities
- Squares and Square Roots
- Step Function
- Subtraction of Decimals
- Types of Functions
- Unit Conversions Measurements
- WordProblemsQE