Operations with Scientific Notation Worksheets - Free Printable

Sure! Let’s solve each problem step by step and express the final answer in scientific notation.

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Problem 1:

(7 × 10⁴)(2 × 10⁶)

Multiply coefficients:
7 × 2 = 14

Add exponents (since same base 10):
10⁴ × 10⁶ = 10⁽⁴⁺⁶⁾ = 10¹⁰

So: 14 × 10¹⁰

But scientific notation requires coefficient between 1 and 10 → convert 14 to 1.4 × 10¹

→ 1.4 × 10¹ × 10¹⁰ = 1.4 × 10¹¹

✔ Answer: 1.4 × 10¹¹

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Problem 2:

(9 × 10⁵) + (5 × 10⁵)

Same exponent → add coefficients:
9 + 5 = 14

→ 14 × 10⁵

Convert to scientific notation:
14 = 1.4 × 10¹ → 1.4 × 10¹ × 10⁵ = 1.4 × 10⁶

✔ Answer: 1.4 × 10⁶

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Problem 3:

(3 × 10⁸) − (7 × 10⁷)

Exponents are different → make them same.

Convert 7 × 10⁷ to match 10⁸:
7 × 10⁷ = 0.7 × 10⁸

Now subtract:
3 × 10⁸ − 0.7 × 10⁸ = (3 − 0.7) × 10⁸ = 2.3 × 10⁸

✔ Answer: 2.3 × 10⁸

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Problem 4:

(5 × 10⁸) / (4 × 10³)

Divide coefficients:
5 ÷ 4 = 1.25

Subtract exponents:
10⁸ ÷ 10³ = 10⁽⁸⁻³⁾ = 10⁵

→ 1.25 × 10⁵

✔ Answer: 1.25 × 10⁵

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Problem 5:

(2 × 10⁴) / (8 × 10²)

Divide coefficients:
2 ÷ 8 = 0.25

Subtract exponents:
10⁴ ÷ 10² = 10²

→ 0.25 × 10²

Convert to scientific notation:
0.25 = 2.5 × 10⁻¹ → 2.5 × 10⁻¹ × 10² = 2.5 × 10¹

✔ Answer: 2.5 × 10¹

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Problem 6:

(2 × 10⁷) − (4 × 10⁷)

Same exponent → subtract coefficients:
2 − 4 = -2

→ -2 × 10⁷

Already in scientific notation (coefficient between 1 and 10 in absolute value).

✔ Answer: -2 × 10⁷

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Problem 7:

(6 × 10⁴) + (1 × 10⁵)

Different exponents → convert to same power.

1 × 10⁵ = 10 × 10⁴

Now:
6 × 10⁴ + 10 × 10⁴ = (6 + 10) × 10⁴ = 16 × 10⁴

Convert: 16 = 1.6 × 10¹ → 1.6 × 10¹ × 10⁴ = 1.6 × 10⁵

✔ Answer: 1.6 × 10⁵

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Problem 8:

(8 × 10⁵)(6 × 10⁷)

Multiply coefficients:
8 × 6 = 48

Add exponents:
10⁵ × 10⁷ = 10¹²

→ 48 × 10¹²

Convert: 48 = 4.8 × 10¹ → 4.8 × 10¹ × 10¹² = 4.8 × 10¹³

✔ Answer: 4.8 × 10¹³

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Problem 9:

(4 × 10⁹)(9 × 10⁵)

Multiply coefficients:
4 × 9 = 36

Add exponents:
10⁹ × 10⁵ = 10¹⁴

→ 36 × 10¹⁴

Convert: 36 = 3.6 × 10¹ → 3.6 × 10¹ × 10¹⁴ = 3.6 × 10¹⁵

✔ Answer: 3.6 × 10¹⁵

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Problem 10:

(3 × 10⁵) + (7 × 10⁷)

Different exponents → convert smaller to match larger.

3 × 10⁵ = 0.03 × 10⁷

Now:
0.03 × 10⁷ + 7 × 10⁷ = (0.03 + 7) × 10⁷ = 7.03 × 10⁷

✔ Answer: 7.03 × 10⁷

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## ✔ Final Answers:

1) 1.4 × 10¹¹
2) 1.4 × 10⁶
3) 2.3 × 10⁸
4) 1.25 × 10⁵
5) 2.5 × 10¹
6) -2 × 10⁷
7) 1.6 × 10⁵
8) 4.8 × 10¹³
9) 3.6 × 10¹⁵
10) 7.03 × 10⁷

Let me know if you’d like a printable version or step-by-step work shown for any specific problem!