Let's solve the questions in the image step-by-step.

Question 1: Rounding Numbers

Round the following to:

• I. 3 significant figures
• II. 2 decimal places

Let's do each one:

Part I: 3 Significant Figures

a) 56210233 → 5.62 × 10⁷
b) 0.00052834 → 5.28 × 10⁻⁴
c) 176.25 → 176
d) 13.8816 → 13.9
e) 0.4625 → 0.463
f) 9.2917 → 9.29
g) 384.728 → 385
h) 1.0009 → 1.00
i) 0.0203 → 0.0203
j) 9738.8925 → 9740

Part II: 2 Decimal Places

a) 56210233 → 56210233.00
b) 0.00052834 → 0.00
c) 176.25 → 176.25
d) 13.8816 → 13.88
e) 0.4625 → 0.46
f) 9.2917 → 9.29
g) 384.728 → 384.73
h) 1.0009 → 1.00
i) 0.0203 → 0.02
j) 9738.8925 → 9738.89

Question 2: Express as Decimal Numbers

Here, we'll convert the numbers in scientific notation to decimal form:

a) 8.71 × 10⁶ = 8,710,000
b) 5.2478 × 10⁴ = 52,478
c) 8.04 × 10⁵ = 804,000
d) 8.32158 × 10⁻⁴ = 0.000832158
e) 2.0 × 10⁻³ = 0.002
f) 6.39 × 10⁻⁶ = 0.00000639
g) 4.7115 × 10³ = 4,711.5
h) 3.22 × 10⁻² = 0.0322
i) 9.305 × 10⁵ = 930,500
j) 7 × 10⁸ = 700,000,000

Question 3: Express in Scientific Notation

Here, we'll convert the numbers to scientific notation:

a) 56210233 = 5.621 × 10⁷
b) 0.00052834 = 5.2834 × 10⁻⁴
c) 176.25 = 1.7625 × 10²
d) 13.8816 = 1.38816 × 10¹
e) 0.4625 = 4.625 × 10⁻¹
f) 9.2917 = 9.2917 × 10⁰
g) 384.728 = 3.84728 × 10²
h) 1392.0009 = 1.3920009 × 10³
i) 0.0203 = 2.03 × 10⁻²
j) 0.000097 = 9.7 × 10⁻⁵

Would you like a detailed explanation for any of these steps or have any questions?

Follow-Up Questions:

1. How do you determine the number of significant figures in a number?
2. What are some common rules for rounding numbers in decimal places?
3. How do you convert a number from scientific notation to its decimal form?
4. Why is scientific notation useful in expressing very large or very small numbers?
5. What are the differences between significant figures and decimal places?

Tip: When working with significant figures, always start counting from the first non-zero digit, whether it is from the left (for numbers greater than 1) or right (for numbers less than 1).