Scientific Notation Worksheets - Math Monks - Free Printable

Let's solve each problem step by step, expressing the answers in scientific notation.

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1) $ (8.41 \times 10^{-5}) - (7.9 \times 10^{-6}) $

We need to subtract two numbers in scientific notation. First, make sure both have the same exponent.

Convert $ 7.9 \times 10^{-6} $ to $ 0.79 \times 10^{-5} $:

$$
8.41 \times 10^{-5} - 0.79 \times 10^{-5} = (8.41 - 0.79) \times 10^{-5} = 7.62 \times 10^{-5}
$$

✔ Answer: $ \boxed{7.62 \times 10^{-5}} $

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2) $ (1.1 \times 10^4) + (7.8 \times 10^5) $

Make exponents the same. Convert $ 1.1 \times 10^4 $ to $ 0.11 \times 10^5 $:

$$
0.11 \times 10^5 + 7.8 \times 10^5 = (0.11 + 7.8) \times 10^5 = 7.91 \times 10^5
$$

✔ Answer: $ \boxed{7.91 \times 10^5} $

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3) $ (9 \times 10^5) + (4.5 \times 10^6) $

Convert $ 9 \times 10^5 $ to $ 0.9 \times 10^6 $:

$$
0.9 \times 10^6 + 4.5 \times 10^6 = (0.9 + 4.5) \times 10^6 = 5.4 \times 10^6
$$

✔ Answer: $ \boxed{5.4 \times 10^6} $

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4) $ \frac{8.1 \times 10^{-2}}{9.0 \times 10^2} $

Divide coefficients and subtract exponents:

$$
\frac{8.1}{9.0} = 0.9, \quad 10^{-2 - 2} = 10^{-4}
$$

So: $ 0.9 \times 10^{-4} $. Convert to proper scientific notation:

$$
0.9 \times 10^{-4} = 9.0 \times 10^{-5}
$$

✔ Answer: $ \boxed{9.0 \times 10^{-5}} $

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5) $ (6 \times 10^3)(9.91 \times 10^0) $

Multiply coefficients and add exponents:

$$
6 \times 9.91 = 59.46, \quad 10^{3+0} = 10^3
$$

So: $ 59.46 \times 10^3 $. Convert to scientific notation:

$$
59.46 \times 10^3 = 5.946 \times 10^4
$$

✔ Answer: $ \boxed{5.946 \times 10^4} $

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6) $ \frac{3 \times 10^{-2}}{8 \times 10^{-1}} $

Divide coefficients and subtract exponents:

$$
\frac{3}{8} = 0.375, \quad 10^{-2 - (-1)} = 10^{-1}
$$

So: $ 0.375 \times 10^{-1} $. Convert to scientific notation:

$$
0.375 \times 10^{-1} = 3.75 \times 10^{-2}
$$

✔ Answer: $ \boxed{3.75 \times 10^{-2}} $

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7) $ (6.0 \times 10^3)(1.5 \times 10^{-2}) $

Multiply coefficients and add exponents:

$$
6.0 \times 1.5 = 9.0, \quad 10^{3 + (-2)} = 10^1
$$

So: $ 9.0 \times 10^1 $

✔ Answer: $ \boxed{9.0 \times 10^1} $

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8) $ (6 \times 10^3) - (11 \times 10^2) $

Convert $ 11 \times 10^2 $ to $ 1.1 \times 10^3 $:

$$
6 \times 10^3 - 1.1 \times 10^3 = (6 - 1.1) \times 10^3 = 4.9 \times 10^3
$$

✔ Answer: $ \boxed{4.9 \times 10^3} $

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9) $ (8.8 \times 10^{-5})^{-5} $

Apply exponent to both coefficient and power of 10:

$$
(8.8)^{-5} \times (10^{-5})^{-5} = 8.8^{-5} \times 10^{25}
$$

Now compute $ 8.8^{-5} $:

First, $ 8.8^5 $:

- $ 8.8^2 = 77.44 $
- $ 8.8^4 = (77.44)^2 \approx 5996.95 $
- $ 8.8^5 = 5996.95 \times 8.8 \approx 52,774.16 $

So $ 8.8^{-5} \approx \frac{1}{52,774.16} \approx 1.9 \times 10^{-5} $

Thus:
$$
(8.8 \times 10^{-5})^{-5} \approx 1.9 \times 10^{-5} \times 10^{25} = 1.9 \times 10^{20}
$$

But let’s be more precise.

Actually, use logarithms or calculator-like steps:

Let’s do it properly:

$$
(8.8 \times 10^{-5})^{-5} = 8.8^{-5} \times 10^{25}
$$

Compute $ 8.8^{-5} $:

$$
8.8^{-5} = \frac{1}{8.8^5}
$$

$ 8.8^2 = 77.44 $

$ 8.8^4 = (77.44)^2 = 5996.9536 $

$ 8.8^5 = 5996.9536 \times 8.8 \approx 52,774.18 $

So $ 8.8^{-5} \approx \frac{1}{52,774.18} \approx 1.9 \times 10^{-5} $

Then:
$$
1.9 \times 10^{-5} \times 10^{25} = 1.9 \times 10^{20}
$$

But better to write as:

$$
(8.8)^{-5} \times 10^{25} = \left(\frac{1}{8.8^5}\right) \times 10^{25} \approx 1.894 \times 10^{-5} \times 10^{25} = 1.894 \times 10^{20}
$$

✔ Answer: $ \boxed{1.89 \times 10^{20}} $ (rounded to three significant figures)

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10) $ (1.6 \times 10^6)(2 \times 10^3) $

Multiply coefficients and add exponents:

$$
1.6 \times 2 = 3.2, \quad 10^{6+3} = 10^9
$$

So: $ 3.2 \times 10^9 $

✔ Answer: $ \boxed{3.2 \times 10^9} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1) | $ 7.62 \times 10^{-5} $ |
| 2) | $ 7.91 \times 10^5 $ |
| 3) | $ 5.4 \times 10^6 $ |
| 4) | $ 9.0 \times 10^{-5} $ |
| 5) | $ 5.946 \times 10^4 $ |
| 6) | $ 3.75 \times 10^{-2} $ |
| 7) | $ 9.0 \times 10^1 $ |
| 8) | $ 4.9 \times 10^3 $ |
| 9) | $ 1.89 \times 10^{20} $ |
| 10) | $ 3.2 \times 10^9 $ |

Let me know if you'd like a PDF version or explanations for any specific step!