Writing Numbers in Scientific Notation (B) Worksheet | PDF ... - Free Printable

Let's solve this step-by-step. The task is to convert numbers into scientific notation.

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🔷 What is Scientific Notation?

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

$$
a \times 10^n
$$

Where:
- $1 \leq |a| < 10$ (a is a number between 1 and 10, including 1 but not 10),
- $n$ is an integer (positive for large numbers, negative for small numbers).

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## ✔ Section A: Large Numbers (Greater than 1)

We move the decimal point to the left until we have a number between 1 and 10. Count how many places you moved — that’s the exponent on 10.

Examples:

- $34000 = 3.4 \times 10^4$ → Move decimal 4 places left.
- $570000 = 5.7 \times 10^5$

Now let's fill out the table.

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🟨 Section A – Answers:

| Number Form | Scientific Notation |
|-------------|---------------------|
| 34000 | $3.4 \times 10^4$ |
| 570000 | $5.7 \times 10^5$ |
| 4780000 | $4.78 \times 10^6$ |
| 65800 | $6.58 \times 10^4$ |
| 789120 | $7.8912 \times 10^5$|
| 6700 | $6.7 \times 10^3$ |
| 11300 | $1.13 \times 10^4$ |
| 999090 | $9.9909 \times 10^5$|
| 23456000 | $2.3456 \times 10^7$|

| Number Form | Scientific Notation |
|-------------|---------------------|
| 78145 | $7.8145 \times 10^4$|
| 3652010 | $3.65201 \times 10^6$|
| 7123444 | $7.123444 \times 10^6$|
| 65.986 | $6.5986 \times 10^1$|
| 241.7111 | $2.417111 \times 10^2$|
| 67.0001 | $6.70001 \times 10^1$|
| 17200.87 | $1.720087 \times 10^4$|
| 2029.003 | $2.029003 \times 10^3$|
| 8162.0892 | $8.1620892 \times 10^3$|

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## ✔ Section B: Small Numbers (Less than 1)

For decimals less than 1, we move the decimal point to the right until we get a number between 1 and 10. The exponent will be negative, and its value is the number of places moved.

Example:

- $0.000234$: Move decimal 4 places right → $2.34 \times 10^{-4}$

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🟨 Section B – Answers:

| Number Form | Scientific Notation |
|-------------|---------------------|
| 0.000234 | $2.34 \times 10^{-4}$ |
| 0.0038791 | $3.8791 \times 10^{-3}$ |
| 0.207813 | $2.07813 \times 10^{-1}$ |
| 0.062192 | $6.2192 \times 10^{-2}$ |
| 0.000701 | $7.01 \times 10^{-4}$ |
| 0.089 | $8.9 \times 10^{-2}$ |
| 0.001187 | $1.187 \times 10^{-3}$ |
| 0.033 | $3.3 \times 10^{-2}$ |
| 0.000046 | $4.6 \times 10^{-5}$ |

| Number Form | Scientific Notation |
|-------------|---------------------|
| 0.891454 | $8.91454 \times 10^{-1}$ |
| 0.042901 | $4.2901 \times 10^{-2}$ |
| 0.000091 | $9.1 \times 10^{-5}$ |
| 0.00000002 | $2 \times 10^{-8}$ |
| 0.0000237 | $2.37 \times 10^{-5}$ |
| 0.00013 | $1.3 \times 10^{-4}$ |
| 0.0000024 | $2.4 \times 10^{-6}$ |
| 0.03600003 | $3.600003 \times 10^{-2}$ |
| 0.0000704 | $7.04 \times 10^{-5}$ |

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✔ Final Answer Summary:

#### Section A (Large Numbers):

- 34000 → $3.4 \times 10^4$
- 570000 → $5.7 \times 10^5$
- 4780000 → $4.78 \times 10^6$
- 65800 → $6.58 \times 10^4$
- 789120 → $7.8912 \times 10^5$
- 6700 → $6.7 \times 10^3$
- 11300 → $1.13 \times 10^4$
- 999090 → $9.9909 \times 10^5$
- 23456000 → $2.3456 \times 10^7$
- 78145 → $7.8145 \times 10^4$
- 3652010 → $3.65201 \times 10^6$
- 7123444 → $7.123444 \times 10^6$
- 65.986 → $6.5986 \times 10^1$
- 241.7111 → $2.417111 \times 10^2$
- 67.0001 → $6.70001 \times 10^1$
- 17200.87 → $1.720087 \times 10^4$
- 2029.003 → $2.029003 \times 10^3$
- 8162.0892 → $8.1620892 \times 10^3$

#### Section B (Small Numbers):

- 0.000234 → $2.34 \times 10^{-4}$
- 0.0038791 → $3.8791 \times 10^{-3}$
- 0.207813 → $2.07813 \times 10^{-1}$
- 0.062192 → $6.2192 \times 10^{-2}$
- 0.000701 → $7.01 \times 10^{-4}$
- 0.089 → $8.9 \times 10^{-2}$
- 0.001187 → $1.187 \times 10^{-3}$
- 0.033 → $3.3 \times 10^{-2}$
- 0.000046 → $4.6 \times 10^{-5}$
- 0.891454 → $8.91454 \times 10^{-1}$
- 0.042901 → $4.2901 \times 10^{-2}$
- 0.000091 → $9.1 \times 10^{-5}$
- 0.00000002 → $2 \times 10^{-8}$
- 0.0000237 → $2.37 \times 10^{-5}$
- 0.00013 → $1.3 \times 10^{-4}$
- 0.0000024 → $2.4 \times 10^{-6}$
- 0.03600003 → $3.600003 \times 10^{-2}$
- 0.0000704 → $7.04 \times 10^{-5}$

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✔ Tips for Success:

- Always make sure the coefficient (a) is between 1 and 10.
- Count how many places you moved the decimal to determine the exponent (n).
- Moving left → positive exponent.
- Moving right → negative exponent.

Let me know if you'd like a printable version or explanation with diagrams!