# 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.

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