Scientific Notation Add and Subtract | PDF | Mathematical Notation ... - Free Printable

To solve these problems, we need to add or subtract numbers in scientific notation. The key is to make sure the powers of 10 are the same before performing the operation. Then, we combine the coefficients and express the final answer in proper scientific notation (a number between 1 and 10 multiplied by a power of 10).

Let’s go through each problem step-by-step.

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Problem 1: (2 × 10³) + (5 × 10⁵)

We can’t add them directly because the exponents are different (3 vs. 5). We convert the smaller exponent to match the larger one.

→ Convert 2 × 10³ to have exponent 5:
2 × 10³ = 0.02 × 10⁵
*(Because 10³ = 10⁵ / 100 → so divide coefficient by 100)*

Now:
= (0.02 × 10⁵) + (5 × 10⁵)
= (0.02 + 5) × 10⁵
= 5.02 × 10⁵ ✔

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Problem 2: (4 × 10⁸) – (9 × 10⁷)

Exponents differ (8 vs. 7). Convert 9 × 10⁷ to exponent 8:

9 × 10⁷ = 0.9 × 10⁸
*(Divide coefficient by 10, multiply exponent by 10 → 10⁷ × 10 = 10⁸)*

Now:
= (4 × 10⁸) – (0.9 × 10⁸)
= (4 – 0.9) × 10⁸
= 3.1 × 10⁸ ✔

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Problem 3: (8 × 10⁹) – (3 × 10⁷)

Convert 3 × 10⁷ to exponent 9:

3 × 10⁷ = 0.03 × 10⁹
*(Divide coefficient by 100 → 10⁷ × 100 = 10⁹)*

Now:
= (8 × 10⁹) – (0.03 × 10⁹)
= (8 – 0.03) × 10⁹
= 7.97 × 10⁹ ✔

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Problem 4: (5 × 10⁷) + (1 × 10⁶)

Convert 1 × 10⁶ to exponent 7:

1 × 10⁶ = 0.1 × 10⁷

Now:
= (5 × 10⁷) + (0.1 × 10⁷)
= (5 + 0.1) × 10⁷
= 5.1 × 10⁷ ✔

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Problem 5: (4 × 10³) + (7 × 10³)

Same exponent! Easy.

= (4 + 7) × 10³
= 11 × 10³

But this is not in proper scientific notation (coefficient must be between 1 and 10).

→ Convert: 11 × 10³ = 1.1 × 10⁴ ✔

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Problem 6: (9 × 10⁵) – (6 × 10⁴)

Convert 6 × 10⁴ to exponent 5:

6 × 10⁴ = 0.6 × 10⁵

Now:
= (9 × 10⁵) – (0.6 × 10⁵)
= (9 – 0.6) × 10⁵
= 8.4 × 10⁵ ✔

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Problem 7: (1 × 10⁶) – (8 × 10⁴)

Convert 8 × 10⁴ to exponent 6:

8 × 10⁴ = 0.08 × 10⁶

Now:
= (1 × 10⁶) – (0.08 × 10⁶)
= (1 – 0.08) × 10⁶
= 0.92 × 10⁶

Not proper scientific notation → adjust:

0.92 × 10⁶ = 9.2 × 10⁵ ✔

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Problem 8: (5 × 10⁹) + (3 × 10⁸)

Convert 3 × 10⁸ to exponent 9:

3 × 10⁸ = 0.3 × 10⁹

Now:
= (5 × 10⁹) + (0.3 × 10⁹)
= (5 + 0.3) × 10⁹
= 5.3 × 10⁹ ✔

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## ✔ Final Answers:

1) 5.02 × 10⁵
2) 3.1 × 10⁸
3) 7.97 × 10⁹
4) 5.1 × 10⁷
5) 1.1 × 10⁴
6) 8.4 × 10⁵
7) 9.2 × 10⁵
8) 5.3 × 10⁹

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📌 Key Tip: Always make sure the powers of 10 are the same before adding or subtracting. Adjust the smaller exponent up by moving the decimal point left in the coefficient (and vice versa for subtraction if needed). Then simplify and convert to proper scientific notation if necessary.