How to Convert a Number from Standard Form to Scientific Notation and Scientific Notation to Standard Form?

Introduction

In ex 2.1 class 9th, students learn important concepts related to numbers and their representation. One of the useful concepts is scientific notation, which provides a convenient way to write very large or very small numbers.

In this article, we will learn how to convert a number from standard form to scientific notation and how to convert a number from scientific notation to standard form.

These notes are especially helpful for students searching for ex 2.1 class 9, 9 class math ex 2.1, and class nine math notes.

Students can also explore other class 9 math notes chapter 1 and chapter-wise learning resources available at Nisar Math Academy.

What is Standard Form?

A number written in its ordinary numerical form is called its standard form.

For example:

• 5,000
• 72,000
• 0.0045
• 0.00072

These are numbers written in standard form.

Large and very small numbers can sometimes be difficult to write and read. Scientific notation gives us a shorter and more convenient way to represent such numbers.

What is Scientific Notation?

Scientific notation is a method of writing a number in the form:

a × 10ⁿ

where:

• a is a number greater than or equal to 1 and less than 10.
• n is an integer.
• 10ⁿ represents a power of 10.

For example:

5,000 = 5 × 10³

Similarly:

0.0045 = 4.5 × 10⁻³

Therefore, scientific notation is particularly useful for representing very large or very small numbers.

How to Convert Standard Form to Scientific Notation?

To convert a number from standard form to scientific notation, follow these steps:

Step 1: Place the decimal point after the first non-zero digit.

Step 2: Count how many places the decimal point has moved.

Step 3: Write the number as a product of the new decimal number and a power of 10.

Step 4: Decide whether the exponent is positive or negative.

• If the decimal point moves to the left, the exponent is positive.
• If the decimal point moves to the right, the exponent is negative.

Example 1: Convert 45,000 into Scientific Notation

Given:

45,000

Move the decimal point after the first non-zero digit:

4.5

The decimal point has moved 4 places to the left.

Therefore:

45,000 = 4.5 × 10⁴

Answer:

4.5 × 10⁴

Example 2: Convert 7,200,000 into Scientific Notation

Given:

7,200,000

Place the decimal point after the first non-zero digit:

7.2

The decimal point moves 6 places to the left.

Therefore:

7,200,000 = 7.2 × 10⁶

Answer:

7.2 × 10⁶

Example 3: Convert 0.0064 into Scientific Notation

Given:

0.0064

Move the decimal point to the right until it comes after the first non-zero digit:

6.4

The decimal point has moved 3 places to the right.

Since the decimal point moved to the right, the exponent is negative.

Therefore:

0.0064 = 6.4 × 10⁻³

Answer:

6.4 × 10⁻³

Example 4: Convert 0.00082 into Scientific Notation

Given:

0.00082

Move the decimal point to the right until it comes after 8:

8.2

The decimal point moves 4 places to the right.

Therefore, the exponent is −4.

So:

0.00082 = 8.2 × 10⁻⁴

Answer:

8.2 × 10⁻⁴

Rule to Remember

A simple rule for converting standard form to scientific notation is:

Large number → Positive exponent

Small number → Negative exponent

For example:

60,000 = 6 × 10⁴

but

0.0006 = 6 × 10⁻⁴

How to Convert Scientific Notation to Standard Form?

To convert a number from scientific notation to standard form, look at the exponent of 10.

If the exponent is positive:

Move the decimal point to the right.

If the exponent is negative:

Move the decimal point to the left.

The number of places you move the decimal point is equal to the value of the exponent.

Example 5: Convert 3.5 × 10⁴ into Standard Form

Given:

3.5 × 10⁴

The exponent is +4, so move the decimal point 4 places to the right.

3.5 → 35 → 350 → 3,500 → 35,000

Therefore:

3.5 × 10⁴ = 35,000

Answer:

35,000

Example 6: Convert 8.2 × 10⁵ into Standard Form

Given:

8.2 × 10⁵

The exponent is positive 5.

Move the decimal point 5 places to the right:

8.2 → 82 → 820 → 8,200 → 82,000 → 820,000

Therefore:

8.2 × 10⁵ = 820,000

Answer:

820,000

Example 7: Convert 4.6 × 10⁻³ into Standard Form

Given:

4.6 × 10⁻³

The exponent is negative 3, so move the decimal point 3 places to the left.

4.6 → 0.46 → 0.046 → 0.0046

Therefore:

4.6 × 10⁻³ = 0.0046

Answer:

0.0046

Example 8: Convert 7.25 × 10⁻⁴ into Standard Form

Given:

7.25 × 10⁻⁴

Move the decimal point 4 places to the left:

7.25 → 0.725 → 0.0725 → 0.00725 → 0.000725

Therefore:

7.25 × 10⁻⁴ = 0.000725

Answer:

0.000725

Difference Between Standard Form and Scientific Notation

Standard Form	Scientific Notation
50,000	5 × 10⁴
720,000	7.2 × 10⁵
0.006	6 × 10⁻³
0.00045	4.5 × 10⁻⁴

Scientific notation makes very large and very small numbers easier to write and handle.

Important Rules for Scientific Notation

1. Scientific notation is written in the form a × 10ⁿ.
2. The value of a must be at least 1 but less than 10.
3. When converting a large number to scientific notation, the exponent is positive.
4. When converting a small decimal number to scientific notation, the exponent is negative.
5. Moving the decimal point to the left gives a positive exponent.
6. Moving the decimal point to the right gives a negative exponent.
7. When converting scientific notation back to standard form, a positive exponent moves the decimal point to the right.
8. A negative exponent moves the decimal point to the left.

Quick Method

Remember this simple pattern:

Standard Form → Scientific Notation

Move decimal point to make the first number between 1 and 10.

Count the moves.

Left → positive exponent

Right → negative exponent

Scientific Notation → Standard Form

Positive exponent → Move decimal point right

Negative exponent → Move decimal point left

Solved Practice Questions

Question 1

Convert 91,000 into scientific notation.

Solution:

91,000 = 9.1 × 10⁴

Question 2

Convert 6,300,000 into scientific notation.

Solution:

6,300,000 = 6.3 × 10⁶

Question 3

Convert 0.00057 into scientific notation.

Solution:

0.00057 = 5.7 × 10⁻⁴

Question 4

Convert 2.4 × 10⁶ into standard form.

Solution:

2.4 × 10⁶ = 2,400,000

Question 5

Convert 8.1 × 10⁻⁵ into standard form.

Solution:

8.1 × 10⁻⁵ = 0.000081

Short Notes

Scientific Notation

Scientific notation is a way of writing very large or very small numbers in the form:

a × 10ⁿ

where 1 ≤ a < 10.

Standard Form to Scientific Notation

• Move the decimal point after the first non-zero digit.
• Count the number of places moved.
• Move left → positive exponent.
• Move right → negative exponent.

Example:

72,000 = 7.2 × 10⁴

0.0072 = 7.2 × 10⁻³

Scientific Notation to Standard Form

• Positive exponent → move decimal point to the right.
• Negative exponent → move decimal point to the left.

Example:

5.6 × 10⁴ = 56,000

5.6 × 10⁻⁴ = 0.00056

MCQs

1. Which of the following is the scientific notation of 50,000?

A. 5 × 10³
B. 5 × 10⁴
C. 50 × 10³
D. 0.5 × 10⁵

Answer: B

2. What is the scientific notation of 0.004?

A. 4 × 10⁻²
B. 4 × 10⁻³
C. 4 × 10³
D. 0.4 × 10⁻²

Answer: B

3. In scientific notation, the first factor must be:

A. Less than 1
B. Equal to 10
C. At least 1 but less than 10
D. Greater than 10

Answer: C

4. What is the standard form of 3.2 × 10⁵?

A. 32,000
B. 320,000
C. 3,200,000
D. 0.00032

Answer: B

5. What is the standard form of 6.4 × 10⁻³?

A. 0.064
B. 0.0064
C. 0.00064
D. 6400

Answer: B

6. When converting a large number into scientific notation, the decimal point generally moves:

A. To the right
B. To the left
C. It does not move
D. Upward

Answer: B

7. When the decimal point moves to the right while converting standard form to scientific notation, the exponent is:

A. Positive
B. Negative
C. Zero
D. Always 1

Answer: B

8. Which is the scientific notation of 8,700,000?

A. 8.7 × 10⁶
B. 8.7 × 10⁷
C. 87 × 10⁶
D. 0.87 × 10⁷

Answer: A

9. Which is the standard form of 7.5 × 10⁻⁴?

A. 0.075
B. 0.0075
C. 0.00075
D. 7500

Answer: C

10. The exponent in 4.2 × 10⁻⁶ is:

A. 6
B. −6
C. 4.2
D. −4.2

Answer: B

Worksheet / Assignment

Part A: Convert Standard Form into Scientific Notation

1. 6,000
2. 45,000
3. 820,000
4. 7,500,000
5. 91,000,000
6. 0.005
7. 0.00072
8. 0.000034
9. 0.0000065
10. 0.00000081

Part B: Convert Scientific Notation into Standard Form

1. 4 × 10³
2. 7.2 × 10⁴
3. 5.6 × 10⁵
4. 8.25 × 10⁶
5. 9.1 × 10⁷
6. 3 × 10⁻²
7. 6.4 × 10⁻³
8. 7.5 × 10⁻⁴
9. 2.8 × 10⁻⁵
10. 9.6 × 10⁻⁶

Part C: Write True or False

1. Scientific notation is written in the form a × 10ⁿ.
2. The first factor in scientific notation can be 15.
3. A positive exponent usually represents a large number.
4. A negative exponent can represent a very small number.
5. 0.005 = 5 × 10⁻³.

Part D: Challenge Questions

Convert the following numbers into scientific notation:

1. 125,000
2. 4,560,000
3. 0.0000092
4. 0.000000305
5. 72,500,000

Then convert your answers back into standard form to check your work.

Conclusion

Understanding scientific notation is an important part of Class 9 Mathematics. Students should remember that the position of the decimal point determines the exponent.

For converting standard form to scientific notation, first make the number between 1 and 10 and then count the decimal places moved.

For converting scientific notation to standard form, use the exponent to determine the direction and number of decimal-point movements.

These concepts are useful for solving questions in ex 2.1 class 9th, ex 2.1 class 9, and 9 class math ex 2.1. Regular practice will help students solve such questions quickly and accurately.

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