# WHOLE NUMBERS NOTATION AND NUMERATION OF NUMBERS

FIRST TERM

Subject:

Term:

Week:

Class:

### JSS 2 (BASIC 8)

Previous lesson:

The pupils have previous knowledge of

POSTURE AND POSTURAL DEFECTS

that was taught as a topic during the last lesson.

Topic :

WHOLE NUMBERS NOTATION AND NUMERATION OF NUMBERS

Behavioural objectives:

At the end of the lesson, the pupils should be able to

• Explain use of whole numbers
• Express whole numbers in standard form
• Convert decimal numbers to standard form
• Changing from standard form to ordinary numbers
• Express numbers in Indices or in index form

## Instructional Materials:

• Wall charts
• Pictures
• Related Online Video
• Flash Cards

Methods of Teaching:

• Class Discussion
• Group Discussion
• Explanation
• Role Modelling
• Role Delegation

Reference Materials:

• Scheme of Work
• Online Information
• Textbooks
• Workbooks
• 9 Year Basic Education Curriculum
• Workbooks

### Content

WHOLE NUMBERS

TOPICS

1. Whole numbers in standard form
2. Decimal numbers in standard form
3. Changing from standard form to ordinary numbers
4. Indices

### WHOLE NUMBERS IN STANDARD FORM

A number is said to be in standard form if it is expressed in the form of A × 10n. Where 1< A < 10 and n is an integer (positive or negative whole numbers). Standard form is very useful in the field of sciences and social sciences for easy presentations and analysis. Examples of numbers in standard form include: 4 × 109, 5.8 × 102, 5.62 × 104, etc.

Examples:

1. Write the following in standard form:

(a) 90 000 000

(b) 6 000 000 000 000 000 000

(c) 34256.189

(d) 879.45

Solutions:

(a) 90 000 000 = 9 × 10 000 000 = 9 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 9 × 107

(b) 6 × 1000 000 000 000 000 000 = 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10  = 6 × 1018

(c) 34256.189 = 3.4256189 × 10 000 = 3.4256189 × 104

(d) 879.45 = 8.7945 × 100 =   8.7945 10 × 10 = 8.7945 × 102

1. Express each of the following in ordinary forms or full figures:

(a) 7.879 × 105

(b) 6.209 × 104

(c) 4.231 × 106

Solutions:

(a) 7.879 × 105 = 7.879 × 10 × 10 × 10 × 10 × 10 = 7.879 × 100 000 = 787900

(b) 6.209 × 104 = 6.209 × 10 × 10 × 10 × 10 = 6.209 × 10 000 = 62090

(c) 4.231 × 106 = 4.231 × 10 × 10 × 10 × 10 × 10 × 10 = 4.231 × 1 000 000 = 42310000

### CLASS ACTIVITY

1. Express the following numbers in standard forms.

(a) 50130002

(b) 0.0000032901

(c) 3518 × 1000000

(d) 0.000400254

(e) 0.000000000235

1. Rewrite each of the following in ordinary forms.

(a) 00009 × 105

(b) 8.543 × 10-4

(c) 6.653 × 10-6

DECIMAL NUMBERS IN STANDARD FORM

Decimal numbers are always written with decimal points. The decimal point is represented with a point. The number of figures that are after the decimal point indicates the number of decimal places that we have in the figure.

Samples

1. 0.345 There is three decimal places in 0.345
2. 34.5 there is one decimal place in 34.5
3. 385.0934 there is four decimal places in 385.0934

Decimal fractions can be expressed in standard form using negative powers of ten (10). This means that the values of when a decimal number is expressed in standard forms are negative. To do this, we move the decimal point to Right Hand Side (RHS) in tenth.

Examples:

1. Express each of these numbers in standard form.

(a) 0.0008

(b) 0.0000 000 7

(c) 0. 000 036

1. Write the following as decimal fractions and standard forms:

(a) 16 thousandths

(b) 60 millionths

Solutions:

(a) 16 thousandths = 1 thousandth × 16 = 0.001 × 16 = 0.0016

In standard form: 0.0016 = 1.6 × 10-3

(b) 60 millionths = 1 millionth × 60 = 0.000001 × 60 = 6 × 10-5

Class activity

1. Rewrite each of the following numbers in figures and put them in standard forms.

(a) 7 thousand

(b) two and one quarter billion

(c) 35 thousandths

(d) 783 millionths

1. Express the following in standard form.

(a) 00000027

(b) 0.000765

(c) 0.0000000000000098

### CHANGING FROM STANDARD FORM TO ORDINARY NUMBERS

Examples:

Express each of the following in ordinary forms or full figures:

(a). 7.879 × 105

(b). 6.209 × 104

(c). 4.231 × 106

Solutions:

(a). 7.879 × 105 = 7.879 × 10 × 10 × 10 × 10 × 10 = 7.879 × 100 000 = 787900

(b). 6.209 × 104 = 6.209 × 10 × 10 × 10 × 10 = 6.209 × 10 000 = 62090

(c). 4.231 × 106 = 4.231 × 10 × 10 × 10 × 10 × 10 × 10 = 4.231 × 1 000 000 = 42310000

Presentation

The topic is presented step by step

Step 1:

The class teacher revises the previous topics

Step 2.

He introduces the new topic

Step 3:

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

EVALUATION:

1. Express the following in standard form:

(a) 000 0004

(b) 720 000 000

(c) 0.000 000 052

(d) 85 000 000 000

1. Express the following in ordinary form

(a) 3 × 108

(b) 2.6 × 107

(c) 4.4 × 109

(d) 3.4 × 105

1. Express the following to decimal fractions

(a) 5 × 10-3

(b) 2.4 × 10-4

(c) 8.8 × 10-5

1. Express the following decimals in standard form

(a) 000 005

(b) 0.0008

(c) 0.000 000 005

1. Simplify the following:

(a) a11 ÷ a9

(b) 3 x 106 × 5 × 103

(c) 2a-1 × (3a)2

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.