**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 1

Example 2

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 3

Convert the following fractions into decimals

**Solution**

Divide the numerator by denominator

Operations and Decimals

Addition of Decimals

Add decimals

Example 4

Evaluate

**Solution**

Subtraction of Decimals

Subtract decimals

Example 5

**Solution**

Multiplication of Decimals

Multiply decimals

Example 6

**Solution**

Mixed Operations with Decimals

Perform mixed operations with decimals

Example 7

**Solution**

Word Problems Involving Decimals

Solve word problems involving decimals

Example 8

If 58 out of 100 students in a school are boys, then write a decimal for the part of the school that consists of boys.

**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 9

**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 10

Convert the following fractions into percentages

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 11

Convert the following percentages into decimals

Percentages in Daily Life

Apply percentages in daily life

Example 12

In an assignment, Regina scored 9 marks out of 12. Express this as a percentage

**Solution**

Example 13

A school has 400 students of which 250 are girls. What percentage of the students are not girls?

**Solution**