Here is a breakdown of the problems from the image, along with their solutions:

1. Write the following numbers in scientific notation:

• (i) 6,200,000 = $6.2 \times 10^6$
• (ii) 91,200 = $9.12 \times 10^4$
• (iii) 4,700,000,000 = $4.7 \times 10^9$
• (iv) 25,780,000 = $2.578 \times 10^7$

2. Write the following numbers in scientific notation:

• (i) 0.00002 = $2 \times 10^{-5}$
• (ii) 0.000000542 = $5.42 \times 10^{-7}$
• (iii) 0.000000093 = $9.3 \times 10^{-8}$
• (iv) 0.003142 = $3.142 \times 10^{-3}$

3. Write the following numbers in normal form:

• (i) 4.12 × 10^4 = 41,200
• (ii) 7.8 × 10^7 = 78,000,000
• (iii) 1.235 × 10^8 = 123,500,000
• (iv) 6.01 × 10^5 = 601,000

4. Write the following numbers in normal form:

• (i) 6 × 10^-5 = 0.00006
• (ii) 5.32 × 10^-4 = 0.000532
• (iii) 9.6 × 10^-8 = 0.000000096
• (iv) 2.102 × 10^-3 = 0.002102

5. Compare: Fill in the blanks with $<, >$ or $=$:

• (i) 2.3 × 10^-6 $<$ 4.65 × 10^-5
• (ii) 7 × 10^-20 $>$ 9 × 10^-21

6. Astronomy: Write the following facts in scientific notation:

• (i) Average diameter of the Earth is 12,756,000 metres = $1.2756 \times 10^7$ metres
• (ii) The temperature at the core of the Sun is 15,600,000 kelvins = $1.56 \times 10^7$ kelvins
• (iii) The population of India as in 2023 is 143 crores = $1.43 \times 10^9$
• (iv) Diameter of an oxygen atom is 0.000000000132 metres = $1.32 \times 10^{-10}$ metres
• (v) Mass of an average human cell is about 0.000000000001 kg = $1 \times 10^{-12}$ kg

7. Multiple Choice Question (MCQ):

The thickness of a soap bubble is about 0.000004 metres. Write the thickness in scientific notation.

• Correct answer: (c) 4 × 10^-6 m

Would you like more details or have any questions on these topics?

Here are some related questions that could help deepen your understanding:

1. How do you convert a number from scientific notation to normal form?
2. What are the common mistakes to avoid when writing numbers in scientific notation?
3. Why is scientific notation useful in astronomy and other sciences?
4. How do you determine the order of magnitude of a number?
5. What are some real-life examples where scientific notation is essential?

Tip: When converting very small numbers to scientific notation, the negative exponent indicates how many places the decimal point has been moved to the right.