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:
- Explain the use of whole numbers.
- Express whole numbers in standard form.
- Convert decimal numbers to standard form.
- Change from standard form to ordinary numbers.
- Express numbers in indices or index form.
Instructional Materials:
- Wall charts
- Pictures
- Related online video
- Flash cards
Methods of Teaching:
- Class discussion
- Group discussion
- Asking questions
- 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:
- 90,000,000
Solution: 90,000,000 = 9 × 10^7 - 6,000,000,000,000,000,000
Solution: 6 × 10^18 - 34,256.189
Solution: 3.4256189 × 10^4 - 879.45
Solution: 8.7945 × 10^2
Express each of the following in ordinary forms or full figures:
- 7.879 × 10^5
Solution: 787,900 - 6.209 × 10^4
Solution: 62,090 - 4.231 × 10^6
Solution: 4,231,000
Class Activity:
Express the following numbers in standard form:
- 50,130,002
- 0.0000032901
- 3,518 × 1,000,000
- 0.000400254
- 0.000000000235
Rewrite each of the following in ordinary form:
- 0.00009 × 10^5
- 8.543 × 10^-4
- 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:
- 0.345 has three decimal places.
- 34.5 has one decimal place.
- 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:
- 0.0008
Solution: 8 × 10^-4 - 0.000000007
Solution: 7 × 10^-9 - 0.000036
Solution: 3.6 × 10^-5
Class Activity:
Rewrite the following numbers in figures and put them in standard form:
- 7 thousand
- Two and one-quarter billion
- 35 thousandths
- 783 millionths
Express the following in standard form:
- 0.00000027
- 0.000765
- 0.0000000000000098
CHANGING FROM STANDARD FORM TO ORDINARY NUMBERS
Examples:
Express each of the following in ordinary forms or full figures:
- 7.879 × 10^5
Solution: 787,900 - 6.209 × 10^4
Solution: 62,090 - 4.231 × 10^6
Solution: 4,231,000
Evaluation
- A number in standard form is expressed as ______.
a) A × 10^n
b) A × 100^n
c) A + 10^n
d) A ÷ 10^n - 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 - 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 - 4.231 × 10^6 in ordinary form is ______.
a) 423,100
b) 4,231,000
c) 42,310,000
d) 4,231 - 8.5 × 10^-3 in ordinary form is ______.
a) 0.0085
b) 0.00085
c) 0.085
d) 85 - The standard form of 90,000,000 is ______.
a) 9 × 10^7
b) 9 × 10^8
c) 9 × 10^6
d) 9 × 10^9 - 5.62 × 10^4 is equal to ______ in ordinary form.
a) 56,200
b) 5,620
c) 562,000
d) 56,200,000 - The number 0.0009 in standard form is ______.
a) 9 × 10^-4
b) 9 × 10^-3
c) 9 × 10^-5
d) 9 × 10^-2 - 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 - The ordinary form of 3 × 10^8 is ______.
a) 30,000,000
b) 3,000,000
c) 300,000,000
d) 3,000 - 7.8 × 10^-5 in ordinary form is ______.
a) 0.000078
b) 0.0000078
c) 0.00078
d) 0.0000087 - 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 - 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 - The ordinary form of 4.5 × 10^3 is ______.
a) 45
b) 450
c) 4,500
d) 45,000 - 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
- 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. - 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. - How do you write 1,000,000 in standard form?
1,000,000 in standard form is written as 1 × 10^6. - What does the exponent represent in standard form?
The exponent indicates how many times the base number (10) is multiplied by itself. - How is 0.00056 written in standard form?
0.00056 in standard form is 5.6 × 10^-4. - 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). - 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. - 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. - 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. - How do you write 0.000003 in standard form?
0.000003 is written as 3 × 10^-6 in standard form. - What is the standard form of 45,000?
The standard form of 45,000 is 4.5 × 10^4. - 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. - What is the ordinary form of 6.7 × 10^5?
The ordinary form of 6.7 × 10^5 is 670,000. - 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). - 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:
- Express the following in standard form:
- 0.000004
- 720,000,000
- 0.000000052
- 85,000,000,000
- Express the following in ordinary form:
- 3 × 10^8
- 2.6 × 10^7
- 4.4 × 10^9
- 3.4 × 10^5
- Express the following to decimal fractions:
- 5 × 10^-3
- 2.4 × 10^-4
- 8.8 × 10^-5
- Express the following decimals in standard form:
- 0.000005
- 0.0008
- 0.000000005
- 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.