# Standard Form in Mathematics Mathematics JSS 2 First Term Lesson Notes Week 1

FIRST TERM LEARNING NOTES

CLASS: JSS 2 (BASIC 8)

SUBJECT: MATHEMATICS

TERM: FIRST TERM

WEEK: WEEK 1

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

Behavioral Objectives:
By the end of the lesson, the pupils should be able to:

1. Explain the use of whole numbers.
2. Express whole numbers in standard form.
3. Convert decimal numbers to standard form.
4. Change from standard form to ordinary numbers.
5. Express numbers in indices or index form.

Instructional Materials:

• Wall charts
• Pictures
• Related online video
• Flash cards

Methods of Teaching:

• Class discussion
• Group discussion
• Explanation
• Role modeling
• Role delegation

Reference Materials:

• Scheme of work
• Online information
• Textbooks
• Workbooks
• 9-Year Basic Education Curriculum

Content:

### WHOLE NUMBERS

Topics:

• Whole numbers in standard form
• Decimal numbers in standard form
• Changing from standard form to ordinary numbers
• Indices

#### WHOLE NUMBERS IN STANDARD FORM

A number is in standard form if it is expressed as A × 10^n, where 1 ≤ A < 10 and n is an integer (positive or negative whole numbers). Standard form is useful in sciences and social sciences for easy presentation and analysis. Examples of numbers in standard form include 4 × 10^9, 5.8 × 10^2, 5.62 × 10^4, etc.

Examples:

Write the following numbers in standard form:

1. 90,000,000
Solution: 90,000,000 = 9 × 10^7
2. 6,000,000,000,000,000,000
Solution: 6 × 10^18
3. 34,256.189
Solution: 3.4256189 × 10^4
4. 879.45
Solution: 8.7945 × 10^2

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

1. 7.879 × 10^5
Solution: 787,900
2. 6.209 × 10^4
Solution: 62,090
3. 4.231 × 10^6
Solution: 4,231,000

Class Activity:

Express the following numbers in standard form:

1. 50,130,002
2. 0.0000032901
3. 3,518 × 1,000,000
4. 0.000400254
5. 0.000000000235

Rewrite each of the following in ordinary form:

1. 0.00009 × 10^5
2. 8.543 × 10^-4
3. 6.653 × 10^-6

### DECIMAL NUMBERS IN STANDARD FORM

Decimal numbers are written with decimal points. The number of figures after the decimal point indicates the number of decimal places.

Examples:

1. 0.345 has three decimal places.
2. 34.5 has one decimal place.
3. 385.0934 has four decimal places.

Decimal fractions can be expressed in standard form using negative powers of ten. This means the values, when expressed in standard form, are negative.

Examples:

1. 0.0008
Solution: 8 × 10^-4
2. 0.000000007
Solution: 7 × 10^-9
3. 0.000036
Solution: 3.6 × 10^-5

Class Activity:

Rewrite the following numbers in figures and put them in standard form:

1. 7 thousand
2. Two and one-quarter billion
3. 35 thousandths
4. 783 millionths

Express the following in standard form:

1. 0.00000027
2. 0.000765
3. 0.0000000000000098

### CHANGING FROM STANDARD FORM TO ORDINARY NUMBERS

Examples:

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

1. 7.879 × 10^5
Solution: 787,900
2. 6.209 × 10^4
Solution: 62,090
3. 4.231 × 10^6
Solution: 4,231,000

### Evaluation

1. A number in standard form is expressed as ______.
a) A × 10^n
b) A × 100^n
c) A + 10^n
d) A ÷ 10^n
2. In standard form, 6,000,000 is written as ______.
a) 6 × 10^7
b) 6 × 10^6
c) 6 × 10^8
d) 6 × 10^5
3. The number 0.000045 in standard form is ______.
a) 4.5 × 10^-5
b) 4.5 × 10^-4
c) 4.5 × 10^5
d) 4.5 × 10^4
4. 4.231 × 10^6 in ordinary form is ______.
a) 423,100
b) 4,231,000
c) 42,310,000
d) 4,231
5. 8.5 × 10^-3 in ordinary form is ______.
a) 0.0085
b) 0.00085
c) 0.085
d) 85
6. The standard form of 90,000,000 is ______.
a) 9 × 10^7
b) 9 × 10^8
c) 9 × 10^6
d) 9 × 10^9
7. 5.62 × 10^4 is equal to ______ in ordinary form.
a) 56,200
b) 5,620
c) 562,000
d) 56,200,000
8. The number 0.0009 in standard form is ______.
a) 9 × 10^-4
b) 9 × 10^-3
c) 9 × 10^-5
d) 9 × 10^-2
9. In standard form, 1,500,000 is written as ______.
a) 1.5 × 10^6
b) 1.5 × 10^7
c) 1.5 × 10^5
d) 1.5 × 10^8
10. The ordinary form of 3 × 10^8 is ______.
a) 30,000,000
b) 3,000,000
c) 300,000,000
d) 3,000
11. 7.8 × 10^-5 in ordinary form is ______.
a) 0.000078
b) 0.0000078
c) 0.00078
d) 0.0000087
12. Which of the following is in standard form?
a) 5.3 × 10^2
b) 53 × 10^1
c) 530 × 10^-1
d) 0.53 × 10^3
13. The decimal number 0.000007 is expressed in standard form as ______.
a) 7 × 10^-7
b) 7 × 10^-6
c) 7 × 10^-8
d) 7 × 10^-5
14. The ordinary form of 4.5 × 10^3 is ______.
a) 45
b) 450
c) 4,500
d) 45,000
15. A number with a negative exponent in standard form will have a value ______ 1.
a) greater than
b) less than
c) equal to
d) none of the above

### Class Activity Discussion

1. What is standard form?
Standard form is a way of writing numbers as a product of a number between 1 and 10 and a power of 10.
2. Why do we use standard form?
We use standard form to simplify the representation of very large or very small numbers, making them easier to work with.
3. How do you write 1,000,000 in standard form?
1,000,000 in standard form is written as 1 × 10^6.
4. What does the exponent represent in standard form?
The exponent indicates how many times the base number (10) is multiplied by itself.
5. How is 0.00056 written in standard form?
0.00056 in standard form is 5.6 × 10^-4.
6. What is the difference between positive and negative exponents in standard form?
A positive exponent means the number is large, while a negative exponent means the number is small (less than 1).
7. Can a number in standard form have more than one digit before the decimal point?
No, in standard form, there is only one non-zero digit before the decimal point.
8. How do you convert a number from standard form to ordinary form?
To convert, you multiply the coefficient by 10 raised to the power of the exponent.
9. Why is standard form important in science?
Standard form is important in science because it allows scientists to handle very large or very small numbers easily.
10. How do you write 0.000003 in standard form?
0.000003 is written as 3 × 10^-6 in standard form.
11. What is the standard form of 45,000?
The standard form of 45,000 is 4.5 × 10^4.
12. How do you determine the exponent when converting to standard form?
The exponent is determined by counting the number of places the decimal point moves to get a number between 1 and 10.
13. What is the ordinary form of 6.7 × 10^5?
The ordinary form of 6.7 × 10^5 is 670,000.
14. Can a number in standard form have a negative exponent?
Yes, a number can have a negative exponent, indicating it is a small number (less than 1).
15. What is the standard form of 0.0000023?
0.0000023 in standard form is 2.3 × 10^-6.

Presentation:

The topic is presented step by step.

Step 1: The teacher revises the previous topics.

Step 2: The teacher introduces the new topic.

Step 3: The teacher allows the pupils to give their own examples and corrects them when needed.

Evaluation:

1. Express the following in standard form:
• 0.000004
• 720,000,000
• 0.000000052
• 85,000,000,000
2. Express the following in ordinary form:
• 3 × 10^8
• 2.6 × 10^7
• 4.4 × 10^9
• 3.4 × 10^5
3. Express the following to decimal fractions:
• 5 × 10^-3
• 2.4 × 10^-4
• 8.8 × 10^-5
4. Express the following decimals in standard form:
• 0.000005
• 0.0008
• 0.000000005
5. Simplify the following:
• a^11 ÷ a^9
• 3 × 10^6 × 5 × 10^3
• 2a^-1 × (3a)^2

Conclusion:

The teacher concludes the lesson by summarizing the topic. The teacher also ensures that the pupils have correctly copied the notes and makes necessary corrections.

Spread the word if you find this helpful! Click on any social media icon to share