# REVISION OF EXPANDED NOTATION

**Subject** :

### Mathematics

**Topic** :

### REVISION OF EXPANDED NOTATION

**Class** :

SS 1

**Term** :

First Term

**Week** :

Week 1

**Instructional Materials** :

- Wall charts
- Online Resources
- Pictures
- Related Audio Visual
- Mathematics Textbooks

**Reference Materials**

- Scheme of Work
- Online Information
- Textbooks
- Workbooks
- Education Curriculum

**Previous Knowledge : **

The pupils have previous knowledge of

### JSS 3 Third Term Examination Mathematics

**Behavioural Objectives :** At the end of the lesson, the pupils should be able to

- explain explain expanded notation of Numbers
- say how to solve simple mental sums on Expanded Notation of Numbers
- Solve simple questions on notation of Numbers with Decimals.

**Content** :

REVISION OF EXPANDED NOTATION

WEEK 1

DATE: ………………….

TOPIC: REVISION OF EXPANDED NOTATION

CONTENT:

## What does Expanded Notation Mean?

Expanded notation can be defined as a way of expressing numbers by showing the value of each digit. Writing a number in expanded notation is not the same as writing in expanded form.

Concept of expanded notation

In expanded notation, a number is represented as the summation of each digit multiplied by its place value, whereas in expanded form, addition is only used between place value numbers. For instance:

732 in expanded form:

= 700 + 30 + 2

while 732 in expanded notation:

= (7 x 100) + (3 x 10) + (2 x 1)

The original form of the number ‘732’ is called a standard form.

Concept of expanded notation:

## How to do Expanded Notation?

To expand a particular number (from its standard form), we need to expand it into the sum of each digit multiplied by its matching place value (ones, tens, hundreds, and so on).

These methods of writing a number in expanded notation and forms are illustrated in the examples below.

= (1 x 10 ^{4}) + (5 x 10 ^{3}) + (8 x 10 ^{2}) + (7 x 10 ^{0})

*Example 5*

Write the thousands, hundreds, tens and ones for each of the following numbers:

a. 945

945 = 9 hundreds + 4 tens + 7 ones

= 900 + 40 + 5

b. 458

458= 4 hundreds + 5 tens + 8 ones

= 400 + 50 + 8

c. 5973

5973 = 5 thousands + 9 hundreds + 7 tens + 3 ones

= 5000 + 900 + 70 + 3

d. 333

333 = 3 hundreds + 3 tens + 3 ones

= 300 + 30 + 3

e. 789

789 = 7 hundreds + 8 tens + 9 ones

= 700 + 80 + 9

Every decimal number X can be expressed uniquely in the form:

This is known as the expanded notation

### Expanded Notation with Decimals

Decimal numbers can also be written in expanded notation by using exponential powers of ten.

*Example 5*

Write 98. 24 in expanded notation?

__Solution__

89.24 = 90 + 6 + 0.2 + 0.04

(8 x 10) + (9 x 1) + (3 x 10 ^{-1}) + (4 x 10 ^{-2})

*Example 6*

Write the decimal number 419.072 in expanded notation.

__Solution__

419.072 = 500 + 30 + 6 + 0.07 + 0.002

(4 x 10 ^{2}) + (1 x 10 ^{1}) + (9 x 10 ^{0}) + (7 x 10 ^{-2}) + (2 x 10 ^{-3})

**Presentation**

The topic is presented step by step

Step 1:

The subject teacher revises the previous topics

Step 2.

He or she introduces the new topic.

Step 3:

The subject teacher allows the pupils to give their own examples and he corrects them when the needs arise

**Evaluation**

- Express the following in expanded notation form

(a) 45078 (b) 0.0235 (c) 930.133 - Write the following in expanded notation form (a)3.456 (b) 0.0042 (c) 856.93
- Write the following decimal numbers in expanded notation (a) 856.93 (b) 749.008 (c) 749.008
- Write the following decimal numbers in an expanded notation form (a) 402 (b) 60.008 (c) 0.0153
- Write in the expanded notation form. (a) 6.666 (b) 315.014(c) 136. 593
- Write the following base ten numbers in expanded notation form (a) 862051 (b) 27654 (c)1077
- Express the following numbers as numbers in the denary scale using expanded form (a)63921(b)939572(c)65293
- Write the following numbers in their ordinary form
- (7 x 10) + (4 x 1) + (9 x 10 -1) + (1 x 10 -2)
- (5 x 10 2) + (4 x 10 1) + (3 x 10 0) + (2 x 10 -2) + (1 x 10 -3)
- (9x 10 2) + (3 x 10 1) + (5 x 10 0) + (7 x 10 -2) + (3 x 10 -3)

**Conclusion** :

The class teacher wraps up or conclude the lesson by giving out short note to summarize the topic that he or she has just taught.

The class teacher also goes round to make sure that the notes are well copied or well written by the pupils.

He or she does the necessary corrections when and where the needs arise.

### REFERENCE TEXTS:

• New General Mathematics for senior secondary schools 1 by M.F Macrae et al; pearson education limited

• New school mathematics for senior secondary school et al; Africana publishers limited