The Concept of Decimals

The Concept of Decimals

Explain the concept of decimals

A decimal- is defined as a number which consist of two parts separated by a point.The parts are whole number part and fractional part

Example

Explain the concept of decimals

Example

Explain the concept of decimals

Conversion of Fractions to Terminating Decimals and Vice Versa

Convert fractions to terminating decimals and vice versa

The first place after the decimal point is called tenths.The second place after the decimal point is called hundredths e.t.c

Consider the decimal number 8.152

NOTE

• To convert a fraction into decimal, divide the numerator by denominator
• To convert a decimal into fraction, write the digits after the decimal point as tenths, or hundredths or thousandths depending on the number of decimal places.

Example

Convert fractions to terminating decimals and vice versa

Solution

Divide the numerator by denominator

Operations and Decimals

Addition of Decimals

Add decimals

Example

Add decimals

Solution

Subtraction of Decimals

Subtract decimals

Example

Subtract decimals

Solution

Multiplication of Decimals

Multiply decimals

Example

Multiply decimals

Solution

Mixed Operations with Decimals

Perform mixed operations with decimals

Example

Perform mixed operations with decimals

Solution

Word Problems Involving Decimals

Solve word problems involving decimals

Example

Solve word problems involving decimals

Solution

We can write a fraction and a decimal for the part of the school that consists of boys.

fraction	decimal
58/100	0.58

Percentages

Expressing a Quantity as a Percentage

Express a quantity as a percentage

The percentage of a quantity is found by converting the percentage to a fraction or decimal and then multiply it by the quantity.

Example

Express a quantity as a percentage

NOTE:The concept of percentage of a quantity can be used to solve the problems involving percentage increase and decrease as shown in the below examples:-

A Fractions into Percentage and Vice Versa

Convert a fraction into percentage and vice versa

To change a fraction or a decimal into a percentage, multiply it by 100%

Example

Convert a fraction into percentage and vice versa

A Decimal into Percentage and Vice Versa

Convert a decimal into percentage and vice versa

To change a percentage into a fraction or a decimal, divide it by 100%

Example

Convert a decimal into percentage and vice versa

Percentages in Daily Life

Apply percentages in daily life

Example

Apply percentages in daily life

Solution

Example

Apply percentages in daily life

Solution