Chemistry worksheet focusing on scientific notation practice.

Let’s solve each part step by step. We’ll go section by section: converting to scientific notation, converting from scientific notation to standard form, and using a calculator for expressions with exponents.

---

Part 1: Express each of the following in scientific notation

Scientific notation means writing a number as:
a × 10ⁿ, where 1 ≤ |a| < 10 and n is an integer.

We move the decimal point so that only one non-zero digit is to the left of the decimal. The number of places we move becomes the exponent (positive if we moved left, negative if we moved right).

1. 0.2 × 10²
First, 0.2 × 100 = 20 → but we want scientific notation.
Better: 0.2 = 2 × 10⁻¹ → so 0.2 × 10² = 2 × 10⁻¹ × 10² = 2 × 10¹
✔ Answer: 2 × 10¹

2. 2.48 × 10³
Already in correct form? Let’s check: 2.48 is between 1 and 10 → yes!
But wait — the problem says “express in scientific notation” — this already is.
However, sometimes they want it simplified or checked. It’s fine.
✔ Answer: 2.48 × 10³

3. 0.56 × 10⁻⁴
0.56 is less than 1 → not proper scientific notation.
Move decimal one place right: 5.6 × 10⁻¹ → then multiply by 10⁻⁴ → total exponent: -1 + (-4) = -5
So: 5.6 × 10⁻⁵
✔ Answer: 5.6 × 10⁻⁵

4. 2.71 × 10⁻⁶
Already good — 2.71 is between 1 and 10.
✔ Answer: 2.71 × 10⁻⁶

5. 3.6 × 10
That’s 3.6 × 10¹ → already scientific notation.
✔ Answer: 3.6 × 10¹

6. 4.462 × 10⁰
10⁰ = 1 → so this is just 4.462 → which is 4.462 × 10⁰ → still valid scientific notation.
✔ Answer: 4.462 × 10⁰

7. 2.87 × 10²
Already good.
✔ Answer: 2.87 × 10²

8. 8.4 × 10⁷
Already good.
✔ Answer: 8.4 × 10⁷

Wait — looking back at the image layout, it seems like there are two columns under Part 1. Let me recheck numbering:

Actually, based on typical worksheet layout, Part 1 has 8 problems labeled 1–8, split into two columns.

So let’s list them clearly:

Left column:
1. 0.2 × 10² → 2 × 10¹
2. 2.48 × 10³ → 2.48 × 10³
3. 0.56 × 10⁻⁴ → 5.6 × 10⁻⁵
4. 2.71 × 10⁻⁶ → 2.71 × 10⁻⁶

Right column:
5. 3.6 × 10 → 3.6 × 10¹
6. 4.462 × 10⁰ → 4.462 × 10⁰
7. 2.87 × 10² → 2.87 × 10²
8. 8.4 × 10⁷ → 8.4 × 10⁷

All done for Part 1.

---

Part 2: Express each of the following in scientific notation

These are regular numbers — convert to scientific notation.

9. 70,000
Move decimal 4 places left → 7.0 × 10⁴
✔ Answer: 7 × 10⁴ (or 7.0 × 10⁴ — both acceptable)

10. 2.9000
This is already between 1 and 10 → 2.9 × 10⁰
But since trailing zeros after decimal may indicate precision, we can write 2.9000 × 10⁰ — but usually we simplify unless told otherwise.
In most cases, 2.9 × 10⁰ is fine.
✔ Answer: 2.9 × 10⁰

11. 200
→ 2 × 10²
✔ Answer: 2 × 10²

12. 0.007
Move decimal 3 places right → 7 × 10⁻³
✔ Answer: 7 × 10⁻³

13. 0.0005
Move decimal 4 places right → 5 × 10⁻⁴
✔ Answer: 5 × 10⁻⁴

14. 5.875
Already between 1 and 10 → 5.875 × 10⁰
✔ Answer: 5.875 × 10⁰

Again, checking layout — likely 6 problems here: 9 to 14.

Left column: 9,10,11 → 70,000; 2.9000; 200
Right column: 12,13,14 → 0.007; 0.0005; 5.875

Done.

---

Part 3: Use your calculator to compute these expressions

We’ll do each one carefully. Remember order of operations and how calculators handle exponents.

15. (302.5)(-0.003)
Multiply: 302.5 × (-0.003) = -0.9075
Now express in scientific notation: -9.075 × 10⁻¹
✔ Answer: -9.075 × 10⁻¹

16. (852)(-0.0002)(-0.01)
First: 852 × (-0.0002) = -0.1704
Then: -0.1704 × (-0.01) = 0.001704
Scientific notation: 1.704 × 10⁻³
✔ Answer: 1.704 × 10⁻³

17. (3.6 × 10⁻⁴)(2.0 × 10⁻⁵)
Multiply coefficients: 3.6 × 2.0 = 7.2
Add exponents: -4 + (-5) = -9
→ 7.2 × 10⁻⁹
✔ Answer: 7.2 × 10⁻⁹

18. (0.002)(0.0002)(-0.01)
First: 0.002 × 0.0002 = 0.0000004
Then: 0.0000004 × (-0.01) = -0.000000004
Which is -4 × 10⁻⁹
✔ Answer: -4 × 10⁻⁹

19. (4.2 × 10⁻³)(7.0 × 10⁻⁵)
Coefficients: 4.2 × 7.0 = 29.4
Exponents: -3 + (-5) = -8
→ 29.4 × 10⁻⁸ → but 29.4 is not between 1 and 10 → adjust:
29.4 = 2.94 × 10¹ → so total: 2.94 × 10¹ × 10⁻⁸ = 2.94 × 10⁻⁷
✔ Answer: 2.94 × 10⁻⁷

20. **(0.0000002)(-0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000