Converting Between Scientific Notation and Ordinary Numbers (Large ... - Free Printable

Sure! Let’s solve the worksheet “Scientific Notation (A)” by converting between scientific notation and ordinary numbers.

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## 📌 Rules to Remember:

➤ To convert scientific notation → ordinary number:

- If exponent is positive, move the decimal point right that many places.
- If exponent is negative, move the decimal point left that many places.
- Add zeros as needed.

➤ To convert ordinary number → scientific notation:

- Move the decimal so there’s one non-zero digit to the left of the decimal.
- Count how many places you moved — that’s your exponent.
- If you moved left, exponent is positive.
- If you moved right, exponent is negative.

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## ✔ SOLUTIONS:

Left Column: Scientific Notation → Ordinary Number

1. 1.23 × 10⁵
→ Move decimal 5 places right:
123,000

2. 9.330
→ Already an ordinary number → 9.330
*(Note: This is likely a trick — it’s not in scientific notation. So just write as is.)*

3. 7.807 × 10⁸
→ Move decimal 8 places right:
780,700,000

4. 3,923,000
→ Wait — this is already ordinary! But looking at the format, it’s on the left side, which should be scientific → probably a typo? Actually, let’s check the layout.

> ⚠️ Important Note: The worksheet has two columns. The left column seems to have scientific notation entries, and the right column has ordinary numbers — but some entries are mixed up.

Actually, re-examining the worksheet:

The instruction says: *“Convert between scientific notation and ordinary numbers.”*

And the layout is:

```
[Scientific Notation] = [Ordinary Number]
```

So each row has one value on the left (to convert to ordinary) and one on the right (to convert to scientific).

Let me reorganize:

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## 🔁 Correct Interpretation:

Each row has two separate conversions:

- Left side: Convert from scientific notation → ordinary number
- Right side: Convert from ordinary number → scientific notation

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## ✍️ Let’s solve row by row:

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Row 1:

- 1.23 × 10⁵ → Move decimal 5 right → 123,000
- 3,450,000 → Move decimal 6 places left → 3.45 × 10⁶

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Row 2:

- 9.330 → This is already ordinary → 9.330
*(But if we interpret it as 9.330 × 10⁰, then it’s still 9.330)*
- 500,000 → Move decimal 5 places left → 5 × 10⁵

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Row 3:

- 7.807 × 10⁸ → Move decimal 8 right → 780,700,000
- 48,000 → Move decimal 4 places left → 4.8 × 10⁴

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Row 4:

- 3,923,000 → Wait — this is ordinary! But it's on the left. Probably meant to be converted TO scientific?
→ 3.923 × 10⁶
- 7.5 × 10⁴ → Move decimal 4 right → 75,000

*(This suggests the worksheet may have formatting issues — some rows have ordinary numbers on left, scientific on right. We’ll follow the pattern: convert what’s given to the other form.)*

Actually, let’s assume each cell needs to be converted to the opposite form regardless of position.

So:

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## ✔ Final Answer Key (Row by Row):

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Row 1:

- 1.23 × 10⁵ → 123,000
- 3,450,000 → 3.45 × 10⁶

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Row 2:

- 9.330 → 9.330 (or 9.33 × 10⁰, but usually left as is)
- 500,000 → 5 × 10⁵

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Row 3:

- 7.807 × 10⁸ → 780,700,000
- 48,000 → 4.8 × 10⁴

---

Row 4:

- 3,923,000 → 3.923 × 10⁶
- 7.5 × 10⁴ → 75,000

---

Row 5:

- 2.6 × 10⁵ → 260,000
- 140,000,000 → 1.4 × 10⁸

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Row 6:

- 4.34 × 10⁵ → 434,000
- 3.09 × 10⁴ → 30,900

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Row 7:

- 879,600 → 8.796 × 10⁵
- 2.2 × 10⁸ → 220,000,000

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Row 8:

- 3.034 × 10⁷ → 30,340,000
- 4.618 × 10⁴ → 46,180

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Row 9:

- 962,000 → 9.62 × 10⁵
- 7.9 × 10⁷ → 79,000,000

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Row 10:

- 6.7 × 10⁵ → 670,000
- 8.4 × 10⁸ → 840,000,000

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## 🧾 Final Answer Sheet:

```
1.23 × 10⁵ = 123,000 | 3,450,000 = 3.45 × 10⁶
9.330 = 9.330 | 500,000 = 5 × 10⁵
7.807 × 10⁸ = 780,700,000 | 48,000 = 4.8 × 10⁴
3,923,000 = 3.923 × 10⁶ | 7.5 × 10⁴ = 75,000
2.6 × 10⁵ = 260,000 | 140,000,000 = 1.4 × 10⁸
4.34 × 10⁵ = 434,000 | 3.09 × 10⁴ = 30,900
879,600 = 8.796 × 10⁵ | 2.2 × 10⁸ = 220,000,000
3.034 × 10⁷ = 30,340,000 | 4.618 × 10⁴ = 46,180
962,000 = 9.62 × 10⁵ | 7.9 × 10⁷ = 79,000,000
6.7 × 10⁵ = 670,000 | 8.4 × 10⁸ = 840,000,000
```

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✔ All conversions completed!

Let me know if you’d like this formatted as a printable answer key or explained with visuals.