**Numbers can be classified in a number of ways.**

1. Natural Numbers- Counting numbers are called natural numbers. Example 1, 2, 3, 4…

2. Whole Numbers- Counting numbers included with zero are whole numbers. Example 0, 1, 2, 3…

3. Integers- All numbers which include zero and positive as well as negative numbers are called integers. Example –2, 3, –1…

4. Real Numbers- All numbers which can be placed on a number line including rational and irrational numbers are called real numbers.

5. Rational Numbers- A rational number is a type of real number that takes the form p/q, where p and q are integers and q is nonzero. Example 2/3, -2/5 etc.

6. Irrational Numbers- Numbers that cannot be expressed as a fraction are irrational numbers. Example: sqrt2 = 1.41421356... is an irrational number.

7. Prime Numbers- A prime number is one whose only factors are 1 and itself. Example: 2, 3, 5, 23 etc.

8. Reciprocal- The reciprocal of a number is obtained when 1 is divided by that number.

9. Square Numbers- Numbers that are raised to the power of two are squares. Example: 5^2=25 or it can be written as 5 x 5 = 5^2.

10. Cube Numbers- Numbers that are raised to the power of 3 are Cube Numbers. Example: 5 x 5 x 5= 125 or it can be represented as 5^3 = 125.

Question: What are square roots and cube roots? Why is it important to study about HCF and LCM?

Answer: HCF is highest common factor which represents highest factor in a group of numbers. LCM is lowest common multiple and it represents lowest multiple in a group. Square and Cube roots are opposite of the squares and cubes. To know the method for finding out HCF, LCM and roots of the number, visit *https://youtube.com/channel/UCoqI7C9rI2UbFPITF2bPgnQ.*

# Accuracy and Approximation

Exact figures are frequently neither essential nor even desirable. In those cases, approximations are provided.

## Rounding off

It is a mathematical operation in which an exact number is rounded to an integer. For Example, if 28569 is a number given then rounding off to 10000 places will give 30000.

## Decimal Places

A number can also be approximated to a predetermined number of decimal places. This is the number of digits following a decimal point.

## Significant Figures

A given number of significant figures can also be used to approximate a number. The most significant figure in the number 43.25 is 4, which has a value of 40. The 5 is the least significant because it only has a value of 5 hundredths.

Question: What are the rules for finding out significant figures?

Answer: There are certain rules when writing significant figures. These rules are important when using scientific notation and writing decimal points. To get information about the rules visit* https://youtube.com/channel/UCoqI7C9rI2UbFPITF2bPgnQ.*

# The Order of Operations

Arithmetic, algebra, and basic geometry are usually taught using simplified expressions. For example, when adding two fractions, the formula for addition is used. The correct order of operations also helps determine the answer of a given question.

When performing mathematical calculations, the numbers one through nine have different values and can be rearranged for other numbers. One of the main things while solving them is to follow BODMAS rule.

BODMAS rule is an acronym for the order of operations. This rule is followed when there is a need to evaluate an equation in which the different types of mathematical operations are used.

BODMAS stands for Brackets, Of, other Division, multiplication, Addition, and subtraction.

# Integers, Fractions, Decimals and Percentages

Fractions are numbers written in the form p/q where p and q are whole numbers and q not equal to zero. Rational numbers are more or like fractions, but in place of whole numbers integers are used.

A fraction whose denominator can be expressed as 100 are percentages. For example, 58/100 can be said as 58%.

To change a fraction to decimal, divide the numerator by denominator. Likewise, when changing a decimal to fraction divide by 10^ number of digits after decimal. For example, 8.65 can be written as 865/100 and then it can be simplified into fraction.

Question: What are recurring decimals and what are the rules to convert recurring decimal to fraction?

Answer: A recurring decimal is one in which the numbers following the decimal point repeat indefinitely. To know how to convert recurring decimal into fraction, visit *https://youtube.com/channel/UCoqI7C9rI2UbFPITF2bPgnQ.*

# Ratio and Proportion

The word ratio simply means relation. A ratio is a comparison between two quantities.

A proportion is the mathematical result of a numerical relationship expressed in the form of =, when two quantities called numerator and denominator are multiplied or divided.

Ratio and proportion are expressed as multiplication or division of the first quantity by the second quantity to the power of one less than the second quantity. Ratio and proportion are solved using unitary method. Sometimes an increase in one quantity causes a decrease in another quantity. This is called inverse proportion.

A compound measure is one made up of two or more other measures.

For Example, Speed= Distance / Time, here speed is directly related to distance and inversely related to time.

# Indices and Standard form

The index denotes the degree to which a number is raised. The integer 5 is raised to the power 3 in Example 53. The number three is known as the index. The plural of index is indices.

Law of Indices:

1. a^m * a^n = a^(m+n)

2. a^m / a^n = a^(m-n)

3. (a^m)^n = a^mn

4. a^-m = 1 / a^m

Also, a^0=1

Exponential Equations: Equations that involve indices as unknowns are known as exponential equations.

# Money and Finance

Earnings: Net pay is the amount that remains after tax, insurance, and pension deductions have been made from gross wages.

Net Pay= Gross Pay – Deductions

Profit and loss

Products are manufactured at a cost known as cost price. They are sold at a selling price. If the selling price is higher then the manufacturer gets the profit otherwise if the product is sold at less price, then there is a loss.