
Standard Form in Mathematics Mathematics JSS 2 First Term Lesson Notes Week 1
FIRST TERM LEARNING NOTES
Table of Contents
ToggleCLASS: 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 Ă— 10^7 - 6,000,000,000,000,000,000
Solution: 6 Ă— 10^18 - 34,256.189
Solution: 3.4256189 Ă— 10^4 - 879.45
Solution: 8.7945 Ă— 10^2
Express each of the following in ordinary forms or full figures:
- 7.879 Ă— 10^5
Solution: 787,900 - 6.209 Ă— 10^4
Solution: 62,090 - 4.231 Ă— 10^6
Solution: 4,231,000
Class Activity:
Express the following numbers in standard form:
- 50,130,002
- 0.0000032901
- 3,518 Ă— 1,000,000
- 0.000400254
- 0.000000000235
Rewrite each of the following in ordinary form:
- 0.00009 Ă— 10^5
- 8.543 Ă— 10^-4
- 6.653 Ă— 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 Ă— 10^-4 - 0.000000007
Solution: 7 Ă— 10^-9 - 0.000036
Solution: 3.6 Ă— 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 Ă— 10^5
Solution: 787,900 - 6.209 Ă— 10^4
Solution: 62,090 - 4.231 Ă— 10^6
Solution: 4,231,000
Evaluation
- A number in standard form is expressed as ______.
a) A Ă— 10^n
b) A Ă— 100^n
c) A + 10^n
d) A Ă· 10^n - In standard form, 6,000,000 is written as ______.
a) 6 Ă— 10^7
b) 6 Ă— 10^6
c) 6 Ă— 10^8
d) 6 Ă— 10^5 - The number 0.000045 in standard form is ______.
a) 4.5 Ă— 10^-5
b) 4.5 Ă— 10^-4
c) 4.5 Ă— 10^5
d) 4.5 Ă— 10^4 - 4.231 Ă— 10^6 in ordinary form is ______.
a) 423,100
b) 4,231,000
c) 42,310,000
d) 4,231 - 8.5 Ă— 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 Ă— 10^7
b) 9 Ă— 10^8
c) 9 Ă— 10^6
d) 9 Ă— 10^9 - 5.62 Ă— 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 Ă— 10^-4
b) 9 Ă— 10^-3
c) 9 Ă— 10^-5
d) 9 Ă— 10^-2 - In standard form, 1,500,000 is written as ______.
a) 1.5 Ă— 10^6
b) 1.5 Ă— 10^7
c) 1.5 Ă— 10^5
d) 1.5 Ă— 10^8 - The ordinary form of 3 Ă— 10^8 is ______.
a) 30,000,000
b) 3,000,000
c) 300,000,000
d) 3,000 - 7.8 Ă— 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 Ă— 10^2
b) 53 Ă— 10^1
c) 530 Ă— 10^-1
d) 0.53 Ă— 10^3 - The decimal number 0.000007 is expressed in standard form as ______.
a) 7 Ă— 10^-7
b) 7 Ă— 10^-6
c) 7 Ă— 10^-8
d) 7 Ă— 10^-5 - The ordinary form of 4.5 Ă— 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 Ă— 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 Ă— 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 Ă— 10^-6 in standard form. - What is the standard form of 45,000?
The standard form of 45,000 is 4.5 Ă— 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 Ă— 10^5?
The ordinary form of 6.7 Ă— 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 Ă— 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 Ă— 10^8
- 2.6 Ă— 10^7
- 4.4 Ă— 10^9
- 3.4 Ă— 10^5
- Express the following to decimal fractions:
- 5 Ă— 10^-3
- 2.4 Ă— 10^-4
- 8.8 Ă— 10^-5
- Express the following decimals in standard form:
- 0.000005
- 0.0008
- 0.000000005
- Simplify the following:
- a^11 Ă· a^9
- 3 Ă— 10^6 Ă— 5 Ă— 10^3
- 2a^-1 Ă— (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, Share This!
- Click to share on Facebook (Opens in new window) Facebook
- Click to share on WhatsApp (Opens in new window) WhatsApp
- Click to share on Telegram (Opens in new window) Telegram
- Click to share on LinkedIn (Opens in new window) LinkedIn
- Click to share on X (Opens in new window) X
- Click to share on X (Opens in new window) X
- More
- Click to email a link to a friend (Opens in new window) Email
- Click to print (Opens in new window) Print
- Click to share on Reddit (Opens in new window) Reddit
- Click to share on Tumblr (Opens in new window) Tumblr
- Click to share on Pinterest (Opens in new window) Pinterest
- Click to share on Pocket (Opens in new window) Pocket
- Click to share on Threads (Opens in new window) Threads
- Click to share on Mastodon (Opens in new window) Mastodon
- Click to share on Nextdoor (Opens in new window) Nextdoor
- Click to share on Bluesky (Opens in new window) Bluesky
Explore Further
Related posts:
- Mastering Indices: An Introduction for JSS 2 Students Mathematics JSS 2 First Term Lesson Notes Week 2
- MATHEMATICS FIRST TERM JSS 2 LESSON NOTES
- Third Term Examinations JSS 2 Mathematic
- REVIEW OF FIRST TERM WORK, EXPANDING AND FACTORIZING ALGEBRAIC EXPRESSIONS, SOLVING OF QUADRATIC EQUATIONS.
- WORD PROBLEMS ON ALGEBRAIC FRACTION
- Algebraic Fractions : Introduction and Expansion of Algebraic Expression
- Trigonometry and Euclidean Geometry ( Pythagorean Theorem)
- Probability JSS 3 Third Term
- Change of Subject in MathematicsÂ
- Mastering Direct and Indirect Variation: A Guide for JSS 2 Students
Related Posts
Differences and Similarities between Colonial Constitutions and Post-Independent Constitutions Third Term Basic 8 JSS 2 Civic Education
1st Term Examination HOME ECONOMICS JSS 2
English Grammar JSS 2 Second Term Examination English Grammar JSS 2 Second Term Lesson Notes
About The Author
Edu Delight Tutors
Am a dedicated educator with a passion for learning and a keen interest in technology. I believe that technology can revolutionize education and am committed to creating an online hub of knowledge, inspiration, and growth for both educators and students. Welcome to Edu Delight Tutors, where learning knows no boundaries.