Scientific Notation Worksheets - Math Monks - Free Printable

Let's solve each problem step by step, following the rules of scientific notation.

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1) Add: (6.91 × 10⁻²) + (2.4 × 10⁻³)

Step 1: Make sure both numbers have the same exponent.
We can convert $2.4 \times 10^{-3}$ to the same power as $10^{-2}$:

$$
2.4 \times 10^{-3} = 0.24 \times 10^{-2}
$$

Now add:
$$
(6.91 + 0.24) \times 10^{-2} = 7.15 \times 10^{-2}
$$

✔ Answer: $7.15 \times 10^{-2}$

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2) Add: (3.4 × 10²) + (4.57 × 10³)

Convert both to the same exponent. Let’s use $10^3$:

$$
3.4 \times 10^2 = 0.34 \times 10^3
$$

Now add:
$$
(0.34 + 4.57) \times 10^3 = 4.91 \times 10^3
$$

✔ Answer: $4.91 \times 10^3$

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3) Subtract: (8.14 × 10⁵) - (7.8 × 10²)

Convert $7.8 \times 10^2$ to $10^5$:

$$
7.8 \times 10^2 = 0.0078 \times 10^5
$$

Now subtract:
$$
(8.14 - 0.0078) \times 10^5 = 8.1322 \times 10^5
$$

✔ Answer: $8.1322 \times 10^5$

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4) Subtract: (5.9 × 10⁻²) - (0.0078 × 10³)

First simplify $0.0078 \times 10^3$:

$$
0.0078 \times 10^3 = 7.8 \times 10^0 = 7.8
$$

Now write $5.9 \times 10^{-2}$ as a decimal:
$$
5.9 \times 10^{-2} = 0.059
$$

Now subtract:
$$
0.059 - 7.8 = -7.741
$$

So:
$$
-7.741 = -7.741 \times 10^0
$$

But we should express it in scientific notation:
$$
-7.741 \times 10^0
$$

✔ Answer: $-7.741 \times 10^0$ or simply $-7.741$

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5) Multiply: (9.2 × 10⁵)(4 × 10⁻³)

Multiply coefficients and add exponents:

$$
(9.2 \times 4) \times 10^{5 + (-3)} = 36.8 \times 10^2
$$

Now convert to proper scientific notation:
$$
36.8 \times 10^2 = 3.68 \times 10^3
$$

✔ Answer: $3.68 \times 10^3$

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6) Multiply: (9.7 × 10⁻³)⁴

Apply exponent to both parts:

$$
(9.7)^4 \times (10^{-3})^4
$$

Calculate $9.7^4$:

- $9.7^2 = 94.09$
- $94.09^2 = 8852.9281$

So:
$$
(9.7)^4 = 8852.9281
$$

Now:
$$
(10^{-3})^4 = 10^{-12}
$$

So:
$$
8852.9281 \times 10^{-12}
$$

Convert to scientific notation:
$$
8.8529281 \times 10^3 \times 10^{-12} = 8.8529281 \times 10^{-9}
$$

✔ Answer: $8.85 \times 10^{-9}$ (rounded to 3 significant figures)

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7) Divide: $\frac{4.6 \times 10^2}{5.01 \times 10^{-3}}$

Divide coefficients and subtract exponents:

$$
\frac{4.6}{5.01} \times 10^{2 - (-3)} = 0.91816... \times 10^5
$$

Convert to proper scientific notation:
$$
0.91816 \times 10^5 = 9.1816 \times 10^4
$$

✔ Answer: $9.18 \times 10^4$ (rounded to 3 significant figures)

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8) Divide: $\frac{2.04 \times 10^{-1}}{2 \times 10^{-2}}$

$$
\frac{2.04}{2} \times 10^{-1 - (-2)} = 1.02 \times 10^{1}
$$

✔ Answer: $1.02 \times 10^1$ or $10.2$

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✔ Final Answers:

1) $7.15 \times 10^{-2}$
2) $4.91 \times 10^3$
3) $8.1322 \times 10^5$
4) $-7.741 \times 10^0$
5) $3.68 \times 10^3$
6) $8.85 \times 10^{-9}$
7) $9.18 \times 10^4$
8) $1.02 \times 10^1$

Let me know if you'd like these written neatly on the worksheet format!